Question

Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.(2, -3). (4, 5)

Answer 1

The equation in slope-intercept form is:

`y=mx+b`

Where m is the slope and b is the y-intercept.

To find it for the given points, we can use this equation to find the slope first:

`m=(y_2-y_1)/(x_2-x_1)`

Since we have the points (2, -3) and (4, 5):

`\begin{gathered} x_1=2_{}_{}_{} \\ y_1=-3 \\ x_2=4 \\ y_2=5 \\ m=(5-(-3))/(4-2)=(5+3)/(2)=(8)/(2)=4 \end{gathered}`

To get to the slope-intercept, we can first use the slope and one of the point to write it in the slope-point form:

`\begin{gathered} y-y_1_{}=m(x-x_1) \\ y+3=4(x-2) \end{gathered}`

And solve for y to get to the answer:

`\begin{gathered} y+3=4x-8 \\ y=4x-11 \end{gathered}`