Question

I need help please.

Answer 1

Answer:

Third Option: $y = \frac{5}{4}x$

Step-by-step explanation:

Given the points on the graph, (4, 5) and (-4, -5):

In order to determine the equation of the given graph in slope-intercept form, y = mx + b:

Use the given points to solve for the slope:

Let (x₁, y₁) = (-4, -5)

(x₂, y₂) = (4, 5)

m = (y₂ - y₁)/(x₂ - x₁)

$m = \frac{5 - (5)}{4 - (-4)} = \frac{5 + 5}{4 + 4} = \frac{10}{8} = \frac{5}{4}$

Therefore, the slope of the line is: $m = \frac{5}{4}$.

Next, use one of the given points on the graph, (4, 5) to solve for the y-intercept, b:

y = mx + b

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

5 = 5 + b

5 - 5 = 5 - 5 + b

0 = b

Therefore, the linear equation in slope-intercept form is: $y = \frac{5}{4}x$.  The correct answer is Option 3.