Home > INT2 > Chapter 3 > Lesson 3.2.4 > Problem3-106

3-106.

Write the equation of the line that has a slope angle of $25^\circ$ and a $y$-intercept of $(0,4)$. Sketch a graph of this line. Assume the slope of the line is positive. . .

$\text{tan (slope angle) }= \left(\frac{\text{opposite side}}{\text{adjacent side}}\right) =\frac{\Delta y}{\Delta x} = \text{slope}$

Since the $\tan(25^\circ)\approx0.466$ then the $\text{slope} ≈ 0.466$

Substitute the slope ($m$) and the $y$-intercept ($b$) in the $y = mx + b$ form for a line.

Note: When a  $y$-intercept is given as a point, the $y$-intercept in an equation is the $y$-coordinate only!

Use the eTool below to graph the line.
Click the link at right for the full version of the eTool: Int2 3-106 HW eTool