Question

The line passing through the points (-2, 10) and (5, -11)

Answer 1

y-intercept = (0, 4)

x-intercept = (3/4, 0)

Explanation:

1 - Find the slope

`slope = m = (rise)/(run) = (y_2~-~y_1)/(x_2~-~x_1) = \frac {-11-10}{5-(-2)} = \frac {-21}{7} = -3`

2 - Plug the slope into y = mx + b and substitute a point into x and y to find the y-intercept, b, by isolating it.

y = mx + b

y = -3x + b

10 = (-3)(-2) + b

10 = 6 + b

-6 -6

4 = b

y-intercept = (0, 4)

3 - Rewrite the completed formula

y = -3x + 4

4 - Substitute 0 in for y to find the x-intercept

0 = -3x + 4

-4 - 4

-4 = -3x

-4/-3 = -3x/-3

4/3 = x

x-intercept = (4/3, 0)