The equation of the line passing through the points [tex](25,3)[/tex] and [tex](-5, -3)[/tex] in slope intercept form is [tex]y=\frac{1}{5}x-2[/tex].
The equation of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is [tex](y-y_1)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex], where [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] represents the slope.
Take [tex](25,3)[/tex] and [tex](-5, -3)[/tex] as [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively.
Put the values in the general equation,
[tex](y-y_1)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
[tex](y-3)=\frac{-3-3}{-5-25} (x-25)[/tex]
[tex](y-3)=\frac{-6}{-30} (x-25)[/tex]
[tex]-30(y-3)=(-6) (x-25)[/tex]
[tex]-30y+90=-6x+150[/tex]
[tex]-30y=-6x+150-90[/tex]
[tex]-30y=-6x+60[/tex]
Slope intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept
[tex]y=\frac{-6}{-30}x+\frac{60}{-30}[/tex]
[tex]y=\frac{1}{5}x-2[/tex]
Learn more about slope-intercept form here:
https://brainly.com/question/9682526?referrer=searchResults
