Question

13. What is the slope-intercept form of the equation of the line shown in the graph?
(3,0)
(0-4)
O A. y = x
O B. y = -4/3x + 4
O C. y = 4/34 - 4
D. y = 3/4x + 3

Answer 1

Answer:

$y=\displaystyle\frac{4}{3}x-4$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x=0)

1) Determine the slope (m)

$m=\displaystyle\frac{y_2-y_1}{x_2-x_1}$ where $(x_1,y_1)$ and $(x_2,y_2)$ are two points that fall on the graph

Plug in the given points (0,-4) and (3,0)

$m=\displaystyle\frac{0-(-4)}{3-0}\\m=\displaystyle\frac{0+4}{3-0}\\m=\displaystyle\frac{4}{3}$

Therefore, the slope of the line is $\displaystyle\frac{4}{3}$. Plug this into $y=mx+b$:

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

2) Determine the y-intercept (b)

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

The y-intercept occurs when x=0. Because we're given that the point (0,-4), we know that the y-intercept is -4. Plug this into the equation:

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

I hope this helps!