Question

Asap answer pls-----------

Answer 1

Answer:

$y=\frac{4}{5}x-\frac{18}{5}$

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 x is 0).

1) Determine the slope (m)

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

In the graph, the points (-3,-6) and (2,-2) are plotted clearly, so we can use these to help us find the slope. Plug them into the equation:

$m=\frac{-6-(-2)}{-3-2}\\m=\frac{-6+2}{-3-2}\\m=\frac{-4}{-5}\\m=\frac{4}{5}$

Therefore, the slope of the line is $\frac{4}{5}$. Plug this into $y=mx+b$ :

$y=\frac{4}{5}x+b$

2) Determine the y-intercept (b)

$y=\frac{4}{5}x+b$

Typically, given a graph, we could look at where exactly the line crosses the y-axis to determine b. However, because it appears ambiguous on this graph, we must solve it algebraically.

Plug in one of the given points (2,-2) and solve for b:

$-2=\frac{4}{5}(2)+b\\-2=\frac{8}{5}+b$

Subtract $\frac{8}{5}$ from both sides to isolate b

$-2-\frac{8}{5}=\frac{8}{5}+b-\frac{8}{5}\\-\frac{18}{5} =b$

Therefore, the y-intercept of the line is $-\frac{18}{5}$. Plug this back into $y=\frac{4}{5}x+b$:

$y=\frac{4}{5}x+(-\frac{18}{5})\\y=\frac{4}{5}x-\frac{18}{5}$

I hope this helps!