First, we can use the slope formula to find the slope of the two points.
[tex]\sf m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
For points in the form of (x1, y1), (x2, y2). Plug in the points:
[tex]\sf m=\dfrac{13-4}{5-2}[/tex]
Subtract:
[tex]\sf m=\dfrac{9}{3}[/tex]
Divide:
[tex]\sf m=3[/tex]
So the slope is 3, we can plug this and one of the points into point-slope form first, and then convert it to slope-intercept form.
[tex]\sf y-y_1=m(x-x_1)[/tex]
Where 'm' is the slope and (x1, y1) is a point on the line. Let's use (2, 4):
[tex]\sf y-4=3(x-2)[/tex]
Now convert to slope-intercept form:
Distribute 3 into the parenthesis:
[tex]\sf y-4=3x-6[/tex]
Add 4 to both sides:
[tex]\boxed{\sf y=3x-2}[/tex]
