Question

Match each equation with its graph. y = 5x + 2, y = 3x + 3, y = 2x + 3

Answer 1

Answer:

All the graphs for each problem

Answer 2

Answer:

Green line: y = 5x + 2

Red line: y = 3x + 3

Purple line: y = 2x + 3

Step-by-step explanation:

1) All the given equations are in slope-intercept form, or $y = mx + b$ format. When an equation is written in this form, the constant on the right side of the equation, or the $b$, represents the y-intercept. The y-intercept is the point at which the line crosses the y-axis.  

Knowing this, the y-intercept of $y = 5x + 2$ must be (0,2). The only graph in which the line crosses the y-axis at the point (0,2) is the one with the green line, thus the graph of $y = 5x + 2$ is the green one.

2) Now, since the other two equations share the same y-intercept, we have two graphs left. We can find out which graph belongs to which equation by taking a look at the slope of the line. The number in place of $m$, or the coefficient of the x-term in an equation in slope-intercept format represents the slope. Thus, the slope of $y = 3x +3$ is 3 and the slope of $y = 2x + 3$ is 2.  

Now, find the slope of one of the lines in the graphs. To do so, use the slope formula,  $m = \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of two points on the  chosen line into the formula in order to figure out the line's slope. I chose to find the slope of the red line, using the points (0,3) and (-1,0):

$m = \frac{(0)-(3)}{(-1)-(0)} \\m = \frac{0-3}{-1-0}\\m = \frac{-3}{-1} \\m = 3$

So, the slope of the red line is 3. Its equation must be $y = 3x + 3$ since it has the matching slope. By process of elimination, the purple line must have the equation of $y = 2x + 3$.