# How do you write an equation in slope intercept form given that the line passes through the point (2,7) and has a slope of 2?

Aug 2, 2018

$y = 2 x + 3$

#### Explanation:

First, write the equation in point-slope form:

Since we are given a point and the slope, we can plug them into the equation:
$y - 7 = 2 \left(x - 2\right)$

Now write it in slope-intercept form:

$y - 7 = 2 x - 4$

Add $\textcolor{b l u e}{7}$ to both sides:
$y - 7 \quad \textcolor{b l u e}{+ \quad 7} = 2 x - 4 \quad \textcolor{b l u e}{+ \quad 7}$

$y = 2 x + 3$

As you can see, this matches the slope-intercept form.

Hope this helps!