Question

Find the equation of the line that satisfies the given conditions.(Lesson 1.10)

Slope$\frac{2}{5}$;y-intercept; 4

Short answer

Equation of the line is $2x-5y+20=0$.

Step-by-step solution

Step 1. Definition of slope-intercept form.

Slope-intercept is the equation of a straight line in the form $y=mx+b$where m is the slope of the line and b is its y-intercept.

Step 2. Plug the value in the equation in a general form.

Use the slope-intercept form to write the equation of the line with $m=\frac{2}{5}$and

$b=4$:

$\begin{array}{l}y=mx+b\\ y=\frac{2}{5}\cdot x+4\end{array}$

Step 3. Calculate the equation of the line in standard form.

$\begin{array}{l}y=\frac{2}{5}x+4\\ 5\cdot y=5\cdot \frac{2}{5}x+5\cdot 4\\ 5y=2x+20\\ -2x+5y-20=0\\ 2x-5y+20=0\end{array}$