Algebra 1b: Unit 3 Obj 4 List The Slope And A Point

1. Find the slope of y + 13 = x

The equation given is in the form y + 13 = x + 1. By rearranging the equation, we can see that y = x - 12. The slope of this equation is 1, which means that for every increase of 1 in the x-coordinate, the y-coordinate will increase by 1 as well. Therefore, the slope of y + 13 = x + 1 is 1.

Explanation

The equation given is in the form y + 13 = x + 1. By rearranging the equation, we can see that y = x - 12. The slope of this equation is 1, which means that for every increase of 1 in the x-coordinate, the y-coordinate will increase by 1 as well. Therefore, the slope of y + 13 = x + 1 is 1.

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3. Find the slope of y = 3/5 (x + 2)

The given equation is in the form y = mx + b, where m represents the slope of the line. In this case, the equation is y = 3/5 (x + 2), which can be rewritten as y = 3/5x + 6/5. Therefore, the slope of the line is 3/5.

Explanation

The given equation is in the form y = mx + b, where m represents the slope of the line. In this case, the equation is y = 3/5 (x + 2), which can be rewritten as y = 3/5x + 6/5. Therefore, the slope of the line is 3/5.

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4. Find the point of y = 3/5 (x + 2)

The given answer, (-2, 0), (-2,0), is the correct point for the equation y = 3/5 (x + 2). This means that when x is equal to -2, y is equal to 0. The equation represents a linear relationship between x and y, where the slope is 3/5 and the y-intercept is 2. Therefore, when x is -2, plugging it into the equation gives y = 3/5 (-2 + 2) = 3/5 * 0 = 0. This confirms that the point (-2, 0) is on the line represented by the equation.

Explanation

The given answer, (-2, 0), (-2,0), is the correct point for the equation y = 3/5 (x + 2). This means that when x is equal to -2, y is equal to 0. The equation represents a linear relationship between x and y, where the slope is 3/5 and the y-intercept is 2. Therefore, when x is -2, plugging it into the equation gives y = 3/5 (-2 + 2) = 3/5 * 0 = 0. This confirms that the point (-2, 0) is on the line represented by the equation.

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5. List the slope of y - 9 = -3(x + 4)

The correct answer is -3. In the given equation, y - 9 = -3(x + 4), the coefficient of x is -3, which represents the slope of the line. Therefore, the slope of the line is -3.

Explanation

The correct answer is -3. In the given equation, y - 9 = -3(x + 4), the coefficient of x is -3, which represents the slope of the line. Therefore, the slope of the line is -3.

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6. List the point of of y - 9 = -3(x + 4)

The given equation is in the form of y - 9 = -3(x + 4), which is the equation of a straight line in slope-intercept form. The equation represents a line with a slope of -3 and a y-intercept of 9. Since the equation does not have any x-term, the value of x can be any real number. Therefore, the line passes through all points with x-coordinate equal to -4 and y-coordinate equal to 9. Thus, the correct answer is (-4, 9), (-4,9).

Explanation

The given equation is in the form of y - 9 = -3(x + 4), which is the equation of a straight line in slope-intercept form. The equation represents a line with a slope of -3 and a y-intercept of 9. Since the equation does not have any x-term, the value of x can be any real number. Therefore, the line passes through all points with x-coordinate equal to -4 and y-coordinate equal to 9. Thus, the correct answer is (-4, 9), (-4,9).

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7. List the slope of y + 7 = 8(x - 3)

The equation y + 7 = 8(x - 3) is in slope-intercept form, y = mx + b, where m represents the slope of the line. In this case, the coefficient of x is 8, which means that the slope of the line is 8.

Explanation

The equation y + 7 = 8(x - 3) is in slope-intercept form, y = mx + b, where m represents the slope of the line. In this case, the coefficient of x is 8, which means that the slope of the line is 8.

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8. List the point of y + 7 = 8(x - 3)

The given equation is in the form y + 7 = 8(x - 3), which represents a linear equation. The answer (3, -7) indicates that when x is equal to 3, y is equal to -7. This means that the point (3, -7) satisfies the equation and lies on the graph of the equation. Therefore, (3, -7) is a valid point for the given equation.

Explanation

The given equation is in the form y + 7 = 8(x - 3), which represents a linear equation. The answer (3, -7) indicates that when x is equal to 3, y is equal to -7. This means that the point (3, -7) satisfies the equation and lies on the graph of the equation. Therefore, (3, -7) is a valid point for the given equation.

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9. List the slope of y - 4 = -6x

The slope of a linear equation can be determined by the coefficient of the x-term. In this equation, y - 4 = -6x, the coefficient of x is -6. Therefore, the slope is -6. The other expressions mentioned, m = -6 and m=-6, are just alternative ways of representing the slope of -6.

Explanation

The slope of a linear equation can be determined by the coefficient of the x-term. In this equation, y - 4 = -6x, the coefficient of x is -6. Therefore, the slope is -6. The other expressions mentioned, m = -6 and m=-6, are just alternative ways of representing the slope of -6.

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11. List the slope and a point on the line from the equation:y - 2 = 3/5 ( x + 9)

M = 3/5 (-2, 9)

M = -3/5 (-2, 9)

M = 3/5 (-9, 2)

M = 3/5 (9, -2)

The equation of the line is given in the form y - 2 = 3/5 (x + 9), which is in slope-intercept form y = mx + b. The slope (m) is 3/5, which is the coefficient of x. The point (-9, 2) is on the line because when we substitute x = -9 into the equation, we get y = 2. Therefore, the correct answer is m = 3/5 (-9, 2).

Explanation

The equation of the line is given in the form y - 2 = 3/5 (x + 9), which is in slope-intercept form y = mx + b. The slope (m) is 3/5, which is the coefficient of x. The point (-9, 2) is on the line because when we substitute x = -9 into the equation, we get y = 2. Therefore, the correct answer is m = 3/5 (-9, 2).

12. List the slope and a point on the line from the equation:y + 8 = 4 ( x - 7)

M = 4 (7, -8)

M = 4 (-7, 8)

M = 4 (8, -7)

M = 4 (-8, 7)

The equation given is in slope-intercept form, y = mx + b, where m is the slope of the line. In this equation, the slope is 4. The point (7, -8) is given in the equation, and it satisfies the equation when substituted into it. Therefore, the correct answer is m = 4 (7, -8).

Explanation

The equation given is in slope-intercept form, y = mx + b, where m is the slope of the line. In this equation, the slope is 4. The point (7, -8) is given in the equation, and it satisfies the equation when substituted into it. Therefore, the correct answer is m = 4 (7, -8).

13. What is the equation in point slope form given the slope is 6 and goes through the point (-4,-16).

Y - 16. = 6(x - 4)

Y + 16 = 6( x +4)

Y - 4 = 6(x - 16)

Y + 4 = 6(x +16)

The equation in point-slope form is y + 16 = 6(x + 4). This is because the point-slope form equation is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the given slope. In this case, the given point is (-4, -16) and the slope is 6. Plugging in these values into the equation gives y + 16 = 6(x + 4).

Explanation

The equation in point-slope form is y + 16 = 6(x + 4). This is because the point-slope form equation is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the given slope. In this case, the given point is (-4, -16) and the slope is 6. Plugging in these values into the equation gives y + 16 = 6(x + 4).