Answer:
[tex]y + 2 = \frac{5}{4} (x + 4)[/tex]
Step-by-step explanation:
1) First, find the slope of the line. Take two points the line intersects and use them for the slope formula, [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. We already know the line intersects (-4, -2). Just choose any one of the points you can see the line intersecting (in this case, I chose (0,3)) and plug in its values, too. Then solve:
[tex]\frac{(3)-(-2)}{(0)-(-4)} \\\frac{3+2}{0+4} \\\frac{5}{4}[/tex]
So, the slope is [tex]\frac{5}{4}[/tex].
2) Now that you have the slope, plug in values for the point-slope formula, [tex]y - y_1 = m (x - x_1)[/tex]. In order to write a linear equation with it, the [tex]x_1[/tex], [tex]y_1[/tex], and [tex]m[/tex] have to be substituted for with real values. The [tex]m[/tex] represents the slope - which means that we should place [tex]\frac{5}{4}[/tex] there. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point - and the questions wants us to use (-4, -2), so substitute -4 for [tex]x_1[/tex] and -2 for [tex]y_1[/tex]:
[tex]y-(-2) = \frac{5}{4} (x - (-4))\\y + 2 = \frac{5}{4} (x + 4)\\[/tex]
Thus, the answer is [tex]y + 2 = \frac{5}{4} (x + 4)[/tex].
