Question

Write an equation that passes through the point (6, -2) with a slope of -4. Write your answer in slope-intercept form.

Answer 1

Given:

a.) An equation that passes through the point (6, -2).

b.) A slope of -4.

Recall, the slope-intercept form:

`\text{ y = mx + b}`

Where,

m = slope

b = y - intercept

x, y = coordinates of the point that pass through the graph

a.) Let's first determine the y-intercept (b). Substitute x, y = 6, -2 and m = -4 in y = mx + b.

`\text{ y = mx + b}`
`\begin{gathered} \text{ (-2) = (-4)(6) + b} \\ \text{ -2 = -24 + b} \\ \text{ -2 + 24 = b} \\ \text{ 22 = b }\rightarrow\text{ b = 22} \end{gathered}`

Therefore, b = 22

b.) Let's now complete the equation. Substitute m = -4 and b = 22 in y = mx + b.

`\text{ y = mx + b}`
`\begin{gathered} \text{ y = (-4)x + (22)} \\ \text{ y = -4x + 22} \end{gathered}`

Therefore, the equation of the line is y = -4x + 22