Question

Passes through (-2,5), slope = -5/7

Answer 1

The slope intercept form of a line is:

$y=mx+b$

Where

m is slope

b in y-intercept

We are already given slope, so we can write:

$y=-\frac{5}{7}x+b$

Now, to figure out b, we replace x with -2 and y with 5 (point given),

$\begin{gathered} y=-\frac{5}{7}x+b \\ 5=-\frac{5}{7}(-2)+b \\ 5=\frac{10}{7}+b \\ b=5-\frac{10}{7} \\ b=\frac{35-10}{7} \\ b=\frac{25}{7} \end{gathered}$

So,

FInal Equation:

$y=-\frac{5}{7}x+\frac{25}{7}$