Question

Write an equation in slope-intercept form of the line that contains the given point and has the given slope.

5. (-2, 2), slope = -5

(0, -2), slope = 1

A. y = -4 - 16x
B. y = - 16
C.4x + y = -16
D. 2x + y = 16
E. y = -6 - 8x
F. y = -16 + 4x

Answer 1

The equation of the line through the point (-2, 2) with slope -5 is y = -5x - 8. The equation of the line through the point (0, -2) with slope 1 is y = x - 2.

Step-by-step explanation:

To write the equation of a line in slope-intercept form, we need the slope and a point on the line. Let's start with the first question.

For the line that contains the point (-2, 2) and has a slope of -5, we can use the slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.

Substituting the given values, we have: y = -5x + b. To find the value of b, we can substitute the coordinates of the given point (-2, 2): 2 = -5(-2) + b. Simplifying, we get 2 = 10 + b. Solving for b, we find b = -8. Therefore, the equation of the line is y = -5x - 8.

For the second question, we are given the point (0, -2) and a slope of 1. Using the same method, we can write the equation of the line as y = 1x + b. Substituting the coordinates, we have -2 = 1(0) + b. Simplifying, we get -2 = 0 + b. Therefore, b = -2. The equation of the line is y = x - 2.