Ecuación De La Recta

1. La casa de Pedro se encuentra en un punto A(-5;2) y el supermercado en un punto B(1;4), Entonces la recta que se forma entre la casa de Pedro y el supermercado es y=-5x+8

True

False

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Explanation

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2. Cuál de las siguientes opciones es la ecuación de la recta que representa a los puntos A(0,6) B(-1,3)

y=3x+6

y=-3x-6

y=6x-3

y=6x+6

The equation of a straight line can be determined using the coordinates of two points on the line. In this case, the points A(0,6) and B(-1,3) are given. To find the equation, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope (m) using the formula (y2 - y1) / (x2 - x1). Substituting the coordinates of A and B, we get (3 - 6) / (-1 - 0) = -3 / -1 = 3.

Next, we substitute the slope (m = 3) and the coordinates of one of the points (A) into the slope-intercept form. Using A(0,6), we have y = 3x + b. Substituting x = 0 and y = 6, we can solve for b: 6 = 3(0) + b, which gives us b = 6.

Therefore, the equation of the line passing through points A(0,6) and B(-1,3) is y = 3x + 6.

Explanation

The equation of a straight line can be determined using the coordinates of two points on the line. In this case, the points A(0,6) and B(-1,3) are given. To find the equation, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope (m) using the formula (y2 - y1) / (x2 - x1). Substituting the coordinates of A and B, we get (3 - 6) / (-1 - 0) = -3 / -1 = 3.

Next, we substitute the slope (m = 3) and the coordinates of one of the points (A) into the slope-intercept form. Using A(0,6), we have y = 3x + b. Substituting x = 0 and y = 6, we can solve for b: 6 = 3(0) + b, which gives us b = 6.

Therefore, the equation of the line passing through points A(0,6) and B(-1,3) is y = 3x + 6.

3. Cuál de las siguientes opciones es la ecuación de la recta que representa a los puntos A(5,-2) B(2,4)

y=2x-8

y=4x+8

y=-2x+8

y=-4x+16

The equation of a line can be determined using the slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the slope is (-2 - 4) / (5 - 2) = -6 / 3 = -2. The y-intercept can be found by substituting the coordinates of one of the points into the equation and solving for b. Using point A (5, -2), we get -2 = -2(5) + b, which gives us b = 8. Therefore, the equation of the line is y = -2x + 8.

Explanation

The equation of a line can be determined using the slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the slope is (-2 - 4) / (5 - 2) = -6 / 3 = -2. The y-intercept can be found by substituting the coordinates of one of the points into the equation and solving for b. Using point A (5, -2), we get -2 = -2(5) + b, which gives us b = 8. Therefore, the equation of the line is y = -2x + 8.

4. Camila tiene una pelota de fútbol y se encuentra parada en un punto con una coordenada de (-4,-2) al patear la pelota esta cae en el punto (5,3), Indique cuál de las siguientes opciones es la ecuación de la recta que se obtiene cuando Camila va a recoger la pelota.

10x-18y+4=0

y=-5x-7

y=-5x+9y-2

5x-9y+2=0

The equation 5x-9y+2=0 represents the line that Camila follows to retrieve the ball. This can be determined by using the coordinates (-4,-2) and (5,3) to find the slope of the line, which is equal to -9/5. The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. By plugging in the slope and one of the given points, we can solve for the y-intercept, which is 2 in this case. Therefore, the equation of the line is 5x-9y+2=0.

Explanation

The equation 5x-9y+2=0 represents the line that Camila follows to retrieve the ball. This can be determined by using the coordinates (-4,-2) and (5,3) to find the slope of the line, which is equal to -9/5. The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. By plugging in the slope and one of the given points, we can solve for the y-intercept, which is 2 in this case. Therefore, the equation of the line is 5x-9y+2=0.

5. Sofía acaba de comprar un nuevo departamento, este se encuentra en el punto A(-2;2), ella actualmente vive en una casa en un punto B(2;5), Entonces la ecuación de la recta que se forma es -3x+4y-14=0

True

False

The given statement is true. The equation of the line formed by the points A(-2,2) and B(2,5) can be found using the slope-intercept form, which is y = mx + b. By rearranging the given equation -3x + 4y - 14 = 0, we can rewrite it as 4y = 3x + 14 and then divide both sides by 4 to get y = (3/4)x + 14/4. This equation represents a line with a slope of 3/4 and a y-intercept of 14/4, which matches the equation of the line passing through the points A and B. Therefore, the statement is true.

Explanation

The given statement is true. The equation of the line formed by the points A(-2,2) and B(2,5) can be found using the slope-intercept form, which is y = mx + b. By rearranging the given equation -3x + 4y - 14 = 0, we can rewrite it as 4y = 3x + 14 and then divide both sides by 4 to get y = (3/4)x + 14/4. This equation represents a line with a slope of 3/4 and a y-intercept of 14/4, which matches the equation of the line passing through the points A and B. Therefore, the statement is true.

6. Cuál de las siguientes opciones es la ecuación de la recta que representa a los puntos A(4;5) B(1;-2)

y=13-7x+3

-7x+3y+13=0

3y-7x=-13

y=7x-13

The correct answer is -7x+3y+13=0. This equation represents the line passing through points A(4,5) and B(1,-2). The equation is in the standard form of a linear equation, where the coefficients of x and y are -7 and 3 respectively. The constant term 13 represents the y-intercept of the line. Therefore, this equation accurately represents the line passing through the given points.

Explanation

The correct answer is -7x+3y+13=0. This equation represents the line passing through points A(4,5) and B(1,-2). The equation is in the standard form of a linear equation, where the coefficients of x and y are -7 and 3 respectively. The constant term 13 represents the y-intercept of the line. Therefore, this equation accurately represents the line passing through the given points.

7. La pendiente de la recta que pasa por tos puntos A(1;2) B(-2;5) es _____

The correct answer is y=-x+3 because the equation of a line can be determined using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the given points A(1,2) and B(-2,5) into the slope formula, we get (-3) / (-3) = 1. Therefore, the slope of the line passing through A and B is 1. Since the line passes through the point (1,2), we can substitute these values into the slope-intercept form to find the equation of the line, which is y = -x + 3.

Explanation

The correct answer is y=-x+3 because the equation of a line can be determined using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the given points A(1,2) and B(-2,5) into the slope formula, we get (-3) / (-3) = 1. Therefore, the slope of the line passing through A and B is 1. Since the line passes through the point (1,2), we can substitute these values into the slope-intercept form to find the equation of the line, which is y = -x + 3.

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8. Cuál de las siguientes opciones es la pendiente de la recta que pasa por los puntos A(-3,2) B(7,-3)

Option 1

Option 2

Option 3

Option 4

The correct answer is Option 1. To find the slope of a line passing through two points, we use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of point A are (-3,2) and the coordinates of point B are (7,-3). Plugging these values into the formula, we get: slope = (-3 - 2) / (7 - (-3)) = -5 / 10 = -1/2. Therefore, the slope of the line passing through points A and B is -1/2.

Explanation

The correct answer is Option 1. To find the slope of a line passing through two points, we use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of point A are (-3,2) and the coordinates of point B are (7,-3). Plugging these values into the formula, we get: slope = (-3 - 2) / (7 - (-3)) = -5 / 10 = -1/2. Therefore, the slope of the line passing through points A and B is -1/2.

9. La pendiente de la recta que atraviesa los puntos A(3;5) B(2;8) es _____

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula (y2 - y1) / (x2 - x1). In this case, the points A(3,5) and B(2,8) are given. Plugging in the values, we get (8 - 5) / (2 - 3) = 3 / -1 = -3. Therefore, the slope of the line passing through the points A and B is -3.

Explanation

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula (y2 - y1) / (x2 - x1). In this case, the points A(3,5) and B(2,8) are given. Plugging in the values, we get (8 - 5) / (2 - 3) = 3 / -1 = -3. Therefore, the slope of the line passing through the points A and B is -3.

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10. La ecuación de la recta que pasa por los puntos A(-3;5) B(2;-4) es _____

The correct answer is y=-1,8x-0,4 , y=9/5x-2/5. This is because the equation of a line passing through two points can be determined using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By calculating the slope between points A and B, we find that it is -1.8. Plugging this slope and the coordinates of point A into the equation, we can solve for the y-intercept, giving us y = -1.8x - 0.4. Similarly, using the slope between points A and B, which is 9/5, and the coordinates of point A, we can determine the y-intercept, resulting in y = 9/5x - 2/5.

Explanation

The correct answer is y=-1,8x-0,4 , y=9/5x-2/5. This is because the equation of a line passing through two points can be determined using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By calculating the slope between points A and B, we find that it is -1.8. Plugging this slope and the coordinates of point A into the equation, we can solve for the y-intercept, giving us y = -1.8x - 0.4. Similarly, using the slope between points A and B, which is 9/5, and the coordinates of point A, we can determine the y-intercept, resulting in y = 9/5x - 2/5.

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Ecuación De LA Recta