# How do you write an equation in slope intercept form given that the line passes through the point (−6, 4) and has a slope of 4/3?

May 30, 2015

The main formula of a line is;
$y = a x + b$

We should use one point to find the real equation. If we use (-6,4) point;
$y = a x + b \implies 4 = - 6 a + b$;
a is the slope of the equation, we found that as $\frac{4}{3}$;
$4 = \left(- 6 \cdot \frac{4}{3}\right) + b \implies 4 = - 8 + b \implies b = 12$;
So the equation of the line will be;
$y = a x + b \implies \underline{y = \frac{4}{3} x + 12}$