Question

What is the y-intercept of the line passing through the point 5, -6 with a slope of -1 over 7

Answer 1

• The y-intercept is (0, -37/7).

Step-by-step 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).