### Home > INT2 > Chapter 3 > Lesson 3.2.5 > Problem3-114

3-114.

Write the equation of the line that has a $33.7^\circ$ slope angle and a $y$-intercept at $(0,7)$. Assume the line has a positive slope.

Sketch a graph and a slope triangle.

$Δx=?$
$Δy=7$

Use the tangent ratio to find the slope:

$\frac{\Delta y}{\Delta x}=\text{slope} = \text{tan}(\theta)$

Once you know the slope and the $y$-intercept, you can write the equation of the line. You use slope-intercept form ($y=mx+b$).

$y \approx \frac{2}{3}x + 7$