The equation of a line can be written in slope-intercept form like this:
y = mx + b
Where m is the slope of the line and b is the Y-intercept. The slope of a line is given by the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case, by taking the points (-9, -9) and (-6, 0) we get:
[tex]m=\frac{0-(-9)}{-6-(-9)}=\frac{0+9}{-6+9}=\frac{9}{3}=3[/tex]
Then we can rewrite the equation of the line like this:
y = 3x + b
By replacing the coordinates of the points (-6, 0) we get:
0 = 3(-6) + b
0 = -18 + b
18 = -18 + 18 + b
18 = b
b = 18
By replacing 18 for b and 3 for m we get:
y = 3x + 18
