Question

Identifying the graph from an Equation of a Line given in y=mx+b format

The graph below is best represented by which equation?
a.) y = 2x+4
b.) y = 1x+4
c.) y = -2x +4
d.) y=-2x-4
Show work

Answer 1

Y=-2x+4, m=-2, b=4
M=-2,b=4

So C is the right answer

Answer 2

C) y = -2x + 4

Explanation:

Slope-intercept form is a common way of representing linear functions.

Slope

As the question states, the equations are in the slope-intercept form: y = mx + b, where m is the slope. So, to find our equation we need to find the slope. Slope is rise over run or the change in y over the change in x. To find the slope we can count the change in y and x between 2 points. We can use points (0,4) and (2,0).

The y-value decreases by 4 and the x-value increases by 2. This creates the slope -4/2. This can be simplified to -2, so m = -2.

Y-Intercept

In y = mx + b, b is the y-intercept. The y-intercept is the y-value where the function intersects with the y-axis. Remember the y-axis is the vertical axis. The y-intercept is also where x = 0.

By looking at the graph, we can tell that the y-intercept is 4. This means that b = 4.

Writing the Equation

Now that we have our values, all we need to do is plug them in. We know that m = -2 and b = 4. So, the equation must be y = -2x + 4.