Question

Pls hlp thx your the best

Answer 1

Jordan earns $10.6 an hour more than Dianelys

Explanation:

As the graph reveals, we're dealing with linear functions where earnings (y) is a function of x:

y = mx + b

Because we want to know how much more Jordan earns per hour than Dianelys, we will need to find the slopes of both lines and subtract.

We can find the slopes of the lines modeling Dianelys and Jordan's earnings using the slope formula:

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )`, were x1 and y1 are one point on the line and x2 and y2 are another point on the line

Dianelys' equation:

We can let (10, 171) be our x1 and y1 point and (20, 342) our x2 and y2 point:

`m=(342-171)/(20-10)\\ m=(171)/(10)\\ m=17.1`

• We know that our b is 0. As the graph shows, when no work is done, Dianelys earns $0. When you're given a graph of a linear function that intersects the y-intercept at (0, 0), you can either stop or verify your answer by plugging in the slope and solving for b and using either one of the points for x and y like (10, 171):

`171=17.1(10)+b\\171=171=b\\0=b`

Thus, the equation modeling Dianelys earnings per hour is y = 17.1x

Jordan's equation:

We can let (10, 277) represent our x1 and y1 point and let (20, 554) represent our x2 and y2 point:

`m=(554-277)/(20-10)\\ m=(277)/(10)\\ m=27.7`

• Like Dianelys equation, we can assume that Jordan's line intersects the y-axis at (0, 0) especially since we're not told something to indicate a b value other than 1 (e.g., "Jordan and Dianelys earn a bonus in addition to their regular wages"):. However, it's important to check by plugging in 27.7 for m and using the point (10, 277) for x and y:

`277=27.7(10)+b\\277=277+b\\0=b`

Thus, the equation modeling Jordan's earnings per hour is y = 27.7x

Finally, we can subtract Dianelys' slope from Jordan's to find how much Jordan earns per hour than Dianelys:

27.7 - 17.1 = 10.6