Answer:
Third Option: [tex]y = \frac{5}{4}x[/tex]
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)
[tex]m = \frac{5 - (5)}{4 - (-4)} = \frac{5 + 5}{4 + 4} = \frac{10}{8} = \frac{5}{4}[/tex]
Therefore, the slope of the line is: [tex]m = \frac{5}{4}[/tex].
Next, use one of the given points on the graph, (4, 5) to solve for the y-intercept, b:
y = mx + b
5 = [tex]\frac{5}{4} (4)[/tex] + b
5 = 5 + b
5 - 5 = 5 - 5 + b
0 = b
Therefore, the linear equation in slope-intercept form is: [tex]y = \frac{5}{4}x[/tex]. The correct answer is Option 3.
