Question

Find the equation of the line passing through the given pair of points. Write the equation in slope-intercept form.(-4,-2), (3,7)

Answer 1

Equation of a line in slope intercept form:

`y=mx+b`

m is the slope

b is the y-intercept

To find the slope use the two given points in the next formula:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ \text{points: }(-4,-2)(3,7) \\ \\ m=(7-(-2))/(3-(-4)) \\ \\ m=(7+2)/(3+4)=(9)/(7) \end{gathered}`

Use the slope and one of the points to find the y-intercept:

`\begin{gathered} y=mx+b \\ (3,7) \\ \\ 7=(9)/(7)(3)+b \\ \\ 7=(27)/(7)+b \\ \\ 7-(27)/(7)=b \\ \\ b=(49-27)/(7) \\ \\ b=(22)/(7) \end{gathered}`

Then, the equation of the line passing through the given pair of points is:

`y=(9)/(7)x+(22)/(7)`