Question

Write the equation of the line passing through the points (25,3) and (-5, -3).

Answer 1

The equation of the line passing through the points $(25,3)$ and $(-5, -3)$ in slope intercept form is $y=\frac{1}{5}x-2$.

The equation of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is $(y-y_1)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$, where $\frac{y_2-y_1}{x_2-x_1}$ represents the slope.

Take $(25,3)$ and $(-5, -3)$ as $(x_1, y_1)$ and $(x_2, y_2)$ respectively.

Put the values in the general equation,

$(y-y_1)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

$(y-3)=\frac{-3-3}{-5-25} (x-25)$

$(y-3)=\frac{-6}{-30} (x-25)$

$-30(y-3)=(-6) (x-25)$

$-30y+90=-6x+150$

$-30y=-6x+150-90$

$-30y=-6x+60$

Slope intercept form is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept

$y=\frac{-6}{-30}x+\frac{60}{-30}$

$y=\frac{1}{5}x-2$

Learn more about slope-intercept form here:

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