Question

What is the equation of the graphed line in point-slope form?

Answer 1

ANSWER

$y - 1 = \frac{2}{3} (x - 3)$

EXPLANATION

To find the equation in point-slope form, use the formula,

$y-y_1=m(x-x_1)$

The $m$
is the slope of the line.

We can read from the graph that, the straight line passes through, the points
$(-3,-3) \: and \: (3,1)$

We can use these two points to find the slope of the line.

The slope can found using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

This means that,

$m = \frac{1 - - 3}{3 - - 3}$

$m = \frac{1 + 3}{3 + 3}$

$m = \frac{4}{6}$

$m = \frac{2}{3}$

We now use one of the points, say
$(3,1)$
with the slope to find the equation of the line.

$y - 1 = \frac{2}{3} (x - 3)$