Question

Find the equation (in terms of xx ) of the line through the points (-2,4) and (3,-5)

Answer 1

Given the points (-2, 4) and (3, -5)

We will find the slope-intercept form of the equation of the line that passes through the given points.

The slope-intercept form is: y = m * x + b

where: m is the slope and (b) is the y-intercept

We will find the slope using the following formula:

`\begin{gathered} slope=(rise)/(run)=(y_2-y_1)/(x_2-x_1) \\ \end{gathered}`

So, the slope will be:

`m=(-5-4)/(3-(-2))=(-9)/(5)`

substitute with (m):

`y=-(9)/(5)x+b`

substitute with the point (3, -5) to find the value of b:

`\begin{gathered} -5=-(9)/(5)\cdot3+b \\ -5=-(27)/(5)+b \\ b=-5+(27)/(5)=(2)/(5) \end{gathered}`

Substitute with (m) and (b) into the slope-intercept form:

So, the answer will be:

`y=-(9)/(5)x+(2)/(5)`