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$y−y_{1}=m(x−x_{1}) $ Here, $m$ is the slope and $(x_{1},y_{1})$ is a point on the line. Thus, to write the equation for the line given by the graph, we must find the slope.

From the graph we can see that two points on the line are $(-2,0)$ and $(3,2).$ To find the slope of the line, we can determine the rise and run between these points.

We can see that, from $(-2,0)$ to $(2,3),$ we move $4$ units to the right and $3$ units up. $runrise =43 ⇔m=-43 $ We can now write the equation in point-slope form. We will substitute the slope $m=43 $ and either one of the points into the equation. We will arbitrarily choose the point $(2,3).$ $y−3=43 (x−2) $

b

From the graph, we can see that two points on the line are $(-4,-2)$ and $(5,1).$ To determine the slope, we'll find the rise and run between the tow points.

We can see that, from $(-3,-1)$ to $(1,2),$ we move $9$ units to the right and $3$ units up. $runrise =93 ⇔m=31 $ We can now write the equation in point-slope form. We will substitute the slope $m=31 $ and either one of the points into the general point-slope form. $y−1=31 (x−5) $