Question

Find an equation for the line below

Answer 1

Answer:

$y=\displaystyle -\frac{1}{4}x+\displaystyle \frac{15}{4}$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept.

1) Determine the slope (m)

$m=\displaystyle \frac{y_2-y_1}{x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

In the graph, two points are indicated: (-5,5) and (3,3). Plug these into the equation:

$m=\displaystyle \frac{3-5}{3-(-5)}\\\\m=\displaystyle \frac{3-5}{3+5}\\\\m=\displaystyle \frac{-2}{8}\\\\m=\displaystyle \frac{-1}{4}$

Therefore, the slope of the line is $\displaystyle -\frac{1}{4}$. Plug this into  $y=mx+b$:

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

2) Determine the y-intercept (b)

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

Plug in one of the points we used earlier and solve for b:

$3=\displaystyle -\frac{1}{4}(3)+b\\\\3=\displaystyle -\frac{3}{4}+b\\\\3+\displaystyle \frac{3}{4}=b\\\\\frac{15}{4} =b$

Therefore, $\displaystyle \frac{15}{4}$ is the y-intercept. Plug this back into $y=\displaystyle -\frac{1}{4}x+b$:

$y=\displaystyle -\frac{1}{4}x+\displaystyle \frac{15}{4}$

I hope this helps!