5-3 Slope-intercept Form Quiz

1. What is the slope intercept form of the equation of the line with slope

1 fourth

and y-intercept at the origin?

The slope-intercept form of the equation of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the y-intercept is at the origin, which means it passes through the point (0,0). Since the y-intercept is 0, the equation simplifies to y = mx. Therefore, the slope-intercept form of the equation of the line with slope m and y-intercept at the origin is y = mx.

Explanation

The slope-intercept form of the equation of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the y-intercept is at the origin, which means it passes through the point (0,0). Since the y-intercept is 0, the equation simplifies to y = mx. Therefore, the slope-intercept form of the equation of the line with slope m and y-intercept at the origin is y = mx.

2. Write the equation of a line that passes through the points (3, 7) and (5, 11).

Y = x + 2

Y = 2x + 1

Y = 2x + 11

The equation of a line can be determined using the slope-intercept form, which is 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) with the given points (3, 7) and (5, 11). The slope is (11 - 7) / (5 - 3) = 4 / 2 = 2. Plugging in the slope and one of the points into the slope-intercept form, we get y = 2x + 1. Therefore, the correct answer is y = 2x + 1.

Explanation

The equation of a line can be determined using the slope-intercept form, which is 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) with the given points (3, 7) and (5, 11). The slope is (11 - 7) / (5 - 3) = 4 / 2 = 2. Plugging in the slope and one of the points into the slope-intercept form, we get y = 2x + 1. Therefore, the correct answer is y = 2x + 1.

3. What is the equation of the line shown below? [image]

Y = 2x - 2

The equation of the line shown below is y = 2x - 2. This equation is in slope-intercept form, where the coefficient of x represents the slope of the line and the constant term represents the y-intercept. In this case, the slope is 2, indicating that for every increase of 1 in x, the y-coordinate increases by 2. The y-intercept is -2, meaning that the line intersects the y-axis at the point (0, -2).

Explanation

The equation of the line shown below is y = 2x - 2. This equation is in slope-intercept form, where the coefficient of x represents the slope of the line and the constant term represents the y-intercept. In this case, the slope is 2, indicating that for every increase of 1 in x, the y-coordinate increases by 2. The y-intercept is -2, meaning that the line intersects the y-axis at the point (0, -2).

4. Which equation represents the line shown?

Y = 5x

Y = -5x

The equation y = -5x represents the line shown because it has a negative slope (-5) and passes through the origin (0,0). This means that as x increases, y decreases at a constant rate. The line is a straight line that slopes downwards from left to right.

Explanation

The equation y = -5x represents the line shown because it has a negative slope (-5) and passes through the origin (0,0). This means that as x increases, y decreases at a constant rate. The line is a straight line that slopes downwards from left to right.

5. What is the slope intercept form of the equation of the line that passes through the point (4, -1) and has an x-intercept of 6?

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates (4, -1) and (6, 0) for (x1, y1) and (x2, y2) respectively, we get m = (-1 - 0) / (4 - 6) = -1 / -2 = 1/2. Since the line passes through the point (4, -1), we can substitute these values into the equation to find b: -1 = (1/2)(4) + b. Solving for b, we get b = -3. Therefore, the slope-intercept form of the equation is y = (1/2)x - 3.

Explanation

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates (4, -1) and (6, 0) for (x1, y1) and (x2, y2) respectively, we get m = (-1 - 0) / (4 - 6) = -1 / -2 = 1/2. Since the line passes through the point (4, -1), we can substitute these values into the equation to find b: -1 = (1/2)(4) + b. Solving for b, we get b = -3. Therefore, the slope-intercept form of the equation is y = (1/2)x - 3.