Question

Find the equation of the line shown.

Answer 1

Answer:

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

Step-by-step explanation:

Equation of a line

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The graph of the picture shows two clear points (-4,-5) and (0,-3). We'll use them to find the required equation:

$\displaystyle y-(-5)=\frac{-3-(-5)}{0-(-4)}(x-(-4))$

Operating:

$\displaystyle y+5=\frac{-3+5}{0+4}(x+4)$

$\displaystyle y+5=\frac{2}{4}(x+4)$

Simplifying the fraction:

$\displaystyle y+5=\frac{1}{2}(x+4)$

Multiplying:

$\displaystyle y+5=\frac{1}{2}x+2$

Solving for y:

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