Question

What is the equation of a line that passes through (0.8) and (3,6)?

Answer 1

Answer:

$y=\frac{-2}{3}x+8$

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 given points $(x_1,y_1)$ are $(x_2,y_2)$

Plug in the given points (0,8) and (3,6)

$m=\frac{6-8}{3-0}\\m=\frac{-2}{3}$

Therefore the slope of the line is $\frac{-2}{3}$. Plug this into $y=mx+b$:

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

2) Determine the y-intercept (b)

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

The y-intercept occurs when x=0. One of the given points is (0,8), so therefore, the y-intercept is 8. Plug this into $y=\frac{-2}{3}x+b$:

$y=\frac{-2}{3}x+8$

I hope this helps!