Question

What is the equation of a line that passes theough the points (-3,4) and (2,8)?​

Answer 1

Explanation

• Find the slope by using rise over run with two given coordinate points.

$\begin{cases} (x_1,y_1)=(-3,4) \\ (x_2,y_2)=(2,8) \end{cases} \\ m = \frac{y_2 - y_1}{x_2 - x_1}$

• Substitute the coordinate values in.

$m = \frac{8 - 4}{2 - ( - 3)} \\ m = \frac{4}{2 + 3} \Longrightarrow \frac{4}{5}$

We have got the value of slope. Substitute in the slope-intercept form.

• Slope-Intercept

$y = mx + b \\ \sf{m = slope}\\ \sf{b = y - intercept}$

Substitute and Rewrite the equation.

$y = \frac{4}{5} x + b$

• Find the y-intercept or the value of b by substituting any given coordinate points.

I will substitute (2,8) in.

$y = \frac{4}{5} x + b \Longrightarrow \sf \small{Substitute \: \: the \: \: coordinate \: \: points \: \: in \: \: the \: \: equation}$

$8 = \frac{4}{5} (2) + b \\ 8 = \frac{8}{5} + b \\ 40 = 8 + 5b \\ 40 - 8 = 5b \\ 32 = 5b \\ \frac{32}{5} = b$

Rewrite the equation by substituting the value of b.

$y = \frac{4}{5} x + \frac{32}{5}$

Answer

$\large \boxed{y = \frac{4}{5} x + \frac{32}{5} }$