Hey there! I'm happy to help!
First, let's find the slope. To find it, you divide the difference in two y values by the difference in the corresponding x values.
The x values are what you can choose. You can choose the number of minutes you choose, but you cannot directly choose the cost. You control the minutes, which dictates what the cost is. So, the minutes are our x values and the costs are our y values.
Let's use the points (500,62) and (750,77).
We subtract the y values.
77-62=15
We subtract the x values.
750-500=250
We divide these.
15/250=0.06
This means that our slope is 0.06, which means that for every minute the cost goes up by six cents.
The slope intercept equation is y=mx+b. The m is slope and b is y-intercept. We already have the slope, but we need the y-intercept. We can plug in the slope and one point on the line to solve for b.
62=0.06(500)+b
Flip the equation so b is on the left.
0.06(500)+b=62
30+b=62
Subtract 30 from both sides.
b=32
Therefore, our equation is y=0.06x+32.
Have a wonderful day! :D
