Answer (assuming the equation can be written in point-slope form):
[tex]y-2 = -\frac{3}{2}(x+6)[/tex]
Step-by-step explanation:
When knowing a point the line crosses through and its slope, you can write an equation in point-slope form, or [tex]y-y_1= m (x-x_1)[/tex].
1) First, find the slope of the line. Use the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] and the x and y values of the two points given, then solve like so:
[tex]\frac{(-1)-(2)}{(-4)-(-6)}\\= \frac{-1-2}{-4+6}\\= \frac{-3}{2}[/tex]
Thus, the slope is [tex]-\frac{3}{2}[/tex].
2) Now, use point-slope form, [tex]y-y_1= m (x-x_1)[/tex]. Substitute the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
The [tex]m[/tex] represents the slope, so substitute [tex]-\frac{3}{2}[/tex] in its place. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line crosses through. Any of the two points will work, and I chose (-6,2) for this answer. So, substitute -6 for
[tex]y-(2)= -\frac{3}{2}(x-(-6)\\y-2 = -\frac{3}{2}(x+6)[/tex]
