Question

1. y-intercept = −1, goes through the point (3, 8)

Answer 1

The y-intercept is (0, -37/7).

Explanation:

When you have one point and the slope of a line you can find its equation by using the point-slope form of the linear function:

m = slope

point = (a, b)

point-slope equation: (y - b) = m (x - a).

Now substitute m = -1/7 and (a,b) = (5, - 6)

y - (-6) = -1/7 (x - 5)

Solve for y:

y + 6 = - 1/7 ( x - 5)

7y + 7(6) = - (x - 5)

7y + 42 = - x + 5

7y = - x + 5 - 42

7y = - x - 37

y = -(1/7)x - 37/7 ← this is the slope-intercept form of the equation.

The y-intercept is the point when x = 0. So, the corresponding y-coordinate is the constant term in the last equation:

y = 0 - 37/7 = - 37/7

And the y-intercept is the point (0, -37/7).