Question

What is the equation of the line in slope-intercept form?

Answer 1

`\displaystyle y = 8x`

Explanation:

Start from the y-intercept of
`\displaystyle [0, 0]`and move eight units south over one unit west. They both are negative integers, so when divided, you get a positive integer:

`\displaystyle 8 = (-8)/(-1)`

Moreover, this function is what is considered direct variation because the graph intersects the origin.

Well, there you have it. I am joyous to assist you at any time.

Answer 2

y = 8x + 0 or y = 8x

Explanation:

Given the graph of a positive-sloped line passing through the point of origin:

In order to determine the linear equation in slope-intercept form, y = mx + b, we must solve for the slope of the line.

Let's use the following points on the graph:

(x₁, y₁) = (0, 0)

(x₂, y₂) = (2, 16)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (16 - 0)/(2 - 0)

m = 16/2

m = 8

Thus, the slope of the line is m = 8.

Next, we must determine the y-intercept, which is the point on the graph where it crosses the y-axis.

The line crosses at the point of origin, (0, 0), which means that the y-intercept, b = 0.

Therefore, the linear equation in slope-intercept form is: y = 8x + 0 or y = 8x.