Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

Answer:

$y=-6x+2$

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 two points that fall on the line are $(x_1,y_1)$ and $(x_2,y_2)$

Given the graph, we determine which points we could use. For example, we could use the two points $(0,2)$ and $(1,-4)$:

$m=\displaystyle \frac{-4-2}{1-0}\\\\m=\displaystyle \frac{-6}{1}\\\\m=-6$

Therefore, the slope of the line is -6. Plug this into $y=mx+b$:

$y=-6x+b$

2) Determine the y-intercept (b)

Recall that the y-intercept occurs when x=0. Given the point (0,2), we know that the y-intercept is 2. Plug this into $y=-6x+b$:

$y=-6x+2$

I hope this helps!