Write a slope intercept equation for a line that passes through (-2,5) and (2,-7)

Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

First, find slope using the given coordinates. Formula for slope: y₁ - y₂ / x₁ - x₂.

Our coordinates are (-2, 5) and (2, - 7). Plug them in and simplify.

5 - (-7) / - 2 - 2

5 + 7 / - 4

12/-4

-3

The slope is - 3. The equation becomes y = - 3x + b.

To find b, plug an (x, y) coordinate on the line in for x and y in the equation and solve. I'll use (-2, 5)

y = - 3x + b

5 = - 3 (-2) + b

5 = 6 + b

-1 = b

The y-intercept is (0, - 1). The equation can now be completed!

Answer:

y = - 3x - 1