Question

QuestionFind the equation of a line that contains the points (-6, 3) and (5,-8). Write the equation in slope-intercept form.

Answer 1

y = -x - 3

STEP BY STEP EXPLANATION

Step 1: The given points are:

(-6, 3) and (5, -8)

Step 2: The slope-intercept form is

`y\text{ = mx + c}`

where m is the slope and c is the intercept

Step 3: Find the slope m

`\begin{gathered} \text{slope (m) = }(y_2-y_1)/(x_2-x_1) \\ \text{m = }\frac{-8_{}-\text{ 3}}{5\text{ - (-6)}} \\ m\text{ = }(-11)/(11)\text{ = -1} \end{gathered}`

Step 4: Solve for intercept c using either of the points

`\begin{gathered} y\text{ = mx + c} \\ c\text{ = y - mx} \\ c\text{ = 3 - (-1)(-6)} \\ c\text{ = 3 - 6} \\ c\text{ = -3} \end{gathered}`

Step 5: Re-writing the slope-intercept form to include the values of m and c

`\begin{gathered} y\text{ = mx + c} \\ y\text{ = -x - 3} \end{gathered}`

Hence, the equation of the line in slope-intercept form is y = -x - 3