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

All the graphs for each problem

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 format. When an equation is written in this form, the constant on the right side of the equation, or the , represents the y-intercept. The y-intercept is the point at which the line crosses the y-axis.  

Knowing this, the y-intercept of 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 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 , or the coefficient of the x-term in an equation in slope-intercept format represents the slope. Thus, the slope of is 3 and the slope of is 2.  

Now, find the slope of one of the lines in the graphs. To do so, use the slope formula,  . 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):

So, the slope of the red line is 3. Its equation must be since it has the matching slope. By process of elimination, the purple line must have the equation of .

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: