Question

I WOULD REALLY APPRECIATE SOME HELP ASAP :)

Alyssa works as a sales representative in an electronics store. She earns a fixed daily wage plus a commission on the sales she makes. The table shows her earnings based on the amount of sales she makes in a day.
The equation that gives Alyssa's daily earnings based on her total sales is____. When this data is plotted on a graph with a line connecting all the points, the y-intercept of the line represents____and the slope of the equation represents____. In this scenario, the y-intercept is____.

Answer 1

We can take any two points from the graph and calculate the slope.


`\sf(y_2-y_1)/(x_2-x_1)`

For any two points in the form of (x1, y1), (x2, y2).

Let's use (0, 80) and (200, 110).


`\sf(110-80)/(200-0)`

Simplify:


`\sf(30)/(200)\rightarrow(3)/(20)`

So this is our slope. Now we can plug this along with one of the points into point-slope form to find our equation:


`\sf y-y_1=m(x-x_1)`

Where 'm' is the slope and (x1, y1) is a point on the line.

Let's use (0, 80):


`\sf y-80=(3)/(20)(x-0)`

Distribute 3/20 into the parenthesis:


`\sf y-80=(3)/(20)x`

Add 80 to both sides:


`\sf y=(3)/(20)x+80` or
`\sf y=0.15x+80`

This is our equation. It's in slope-intercept form, y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

So the y-intercept is 80, it represents what 'y' is(daily earnings) when 'x'(total sales) is 0, so this must be her fixed wage rate.

And the slope is 0.15, which represents for every change in x, there is a 0.15 * x change in y. This is her rate of commission, she gets 15 cents for every sale.