Question

What is an equation of the line that passes through the points (6,-6) and (-2,-2)

Answer 1

Answer:

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

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 (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

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

Plug in the given points (6,-6) and (-2,-2)

$=\frac{-2-(-6)}{-2-6}\\=\frac{-2+6}{-2-6}\\=\frac{4}{-8}\\=-\frac{1}{2}$

Therefore, the slope of the line is $-\frac{1}{2}$. Plug this into $y=mx+b$:

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

2) Determine the y-intercept (b)

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

Plug in one of the given points and solve for b

$-6=-\frac{1}{2}(6)+b\\-6=-3+b$

Add 3 to both sides

$-6+3=-3+b+3\\-3=b$

Therefore, the y-intercept of the line is -3. Plug this back into $y=-\frac{1}{2}x+b$:

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

I hope this helps!