Question

Which equation does the graph below represent?

y = 1/4 + x

y = 1/4x

y = 4 + x

y = 4x

Answer 1

`\boxed{y=4x}`

Explanation:

First, lets see where the line crosses the y-axis at, the line crosses the y-axis at (0, 0), the y-intercept is 0.

We can use slope-intercept form of the equation to solve.

y = mx + b

m = slope

b = y-intercept

We know b = 0

y = mx + 0

y = mx

We need to find the slope.

slope = rise/run

Take two points: (0, 0) and (1, 4)

m = (4 - 0)/(1 - 0)

m = 4/1

m = 4

The slope of the line is 4.

y = (4)x

y = 4x

Answer 2

y = 4x

Explanation:

If you look at the graph, it is crossing the y-axis at the origin of (0, 0). This means that the y-intercept (or the "b" in your equation of y = mx + b) will be zero. Since it is a zero, it would not need to be in the equation.

So, right now we have y = mx + 0, which would simply be just y = mx.

Next, remember that the "m" in this equation represents the slope. To find the slope on a graph, it is calculated by rise over run. If you look at your graph, starting at the origin, the rise is going up 4 units and the run is over by 1. This makes your slope (or your "m" value) the fraction of 4 over 1 (4/1).

This slope can simply be written as 4 because we know that anything over 1 is just equal to the numerator value.

So, this makes the equation for this line in slope intercept form as the following:

y = mx + b

y = (4/1)x + 0

y = 4x