Answer:
[tex]y = \frac{1}{2}x-3\\[/tex]
Step-by-step explanation:
To write an equation in slope-intercept form with the given information, first write the equation in point-slope form, then transfer it to slope-intercept form.
1) First, find the slope. Using the x and y values of the two points given, substitute them in the correct order into the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] and solve:
[tex]\frac{(-12)-(-14)}{(-18)-(-22)} \\= \frac{-12+14}{-18 + 22} \\= \frac{2}{4} \\= \frac{1}{2}[/tex]
Thus, the slope is [tex]\frac{1}{2}[/tex].
2) Now that we know the slope and at least one point the line intersects, use the point-slope form [tex]y-y_1 = m (x-x_1)[/tex] .
Since [tex]m[/tex] represents the slope, substitute it for [tex]\frac{1}{2}[/tex] in the equation. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, substitute the x and y values of one of the given points into the equation as well. (Either point is fine, and I chose (-18, -12) as seen below.) Afterwards, isolate y to get the following answer and equation:
[tex]y - (-12) = \frac{1}{2} (x-(-18))\\y + 12 = \frac{1}{2} (x + 18)\\y + 12 = \frac{1}{2} x + 9 \\y = \frac{1}{2} x -3[/tex]
