Question

Use the point-slope formula to write an equation of the line that passes through (-4,9) and has a slope of m-2. Write the answer in slope-intercept form (ifpossible)

Answer 1

A linear equation the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

To find "m" and "b", follow the steps below.

Step 01: Substitute the slope in the equation.

According to the problem, the slope is -2. That is, m = -2.

Then,

`y=-2x+b`

Step 02: Substitute the point (-4, 9) in the equation.

(-4, 9) means x = -4 and y = 9. Then,

`\begin{gathered} 9=-2\cdot(-4)+b \\ 9=8+b \end{gathered}`

Subtract 8 from both sides to find b.

`\begin{gathered} 9-8=8+b-8 \\ 1=0+b \\ 1=b \end{gathered}`

Substituting "m" and "b" in the equation:

`y=-2x+1`

Answer:

`y=-2x+1`