Question

Write an equation of the line in slope-intercept form.

Answer 1

Answer:

$\displaystyle y=\frac{1}{3}x+\frac{4}{3}$

Step-by-step explanation:

Equation of a line

The slope-intercept form of a line is:

y=mx+b

Where m is the slope and b is the y-intercept.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated as follows:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Two points are given: (-4,0) (2,2). Calculate the slope:

$\displaystyle m=\frac{2-0}{2+4}=\frac{2}{6}=\frac{1}{3}$

We'll use the point-slope form of the line:

y-k=m(x-h)

Take the point (2,2):

$\displaystyle y-2=\frac{1}{3}(x-2)$

Operating:

$\displaystyle y-2=\frac{1}{3}x-\frac{2}{3}$

Adding 2:

$\displaystyle y=\frac{1}{3}x-\frac{2}{3}+2$

Operating, we get the slope-intercept form:

$\boxed{\displaystyle y=\frac{1}{3}x+\frac{4}{3}}$