Question

Helppp I can’t solve this….

Answer 1

So we're trying to find the equation of a line using the provided x and y values in the chart. We should start by finding the slope of the line, since that's easiest!

We know that the equation for slope is
`m=(rise)/(run)=(y_2-y_1)/(x_2-x_1)`

All we need to do is pick two points (two x and y coordinates) and respectively plug them into the equation! I want to note that it does not matter which two points you choose! You will always get the same slope!

Alright, so using the two points (-2, -17) and (0, 23) I'll calculate the slope!

`m=(y_2-y_1)/(x_2-x_1)\\m=(23-(-17))/(0-(-2))\\m=(23+17)/(0+2)\\m=(40)/(2)\\m=20`

(Just to prove that you can use any two points I'm going to do another example. The only thing you need to keep in mind is that y values are always on top and x values are always on the bottom! In this example I'm using (-6, -97) and (2,63)!)

`m=(63-(-97))/(2-(-6))\\m=(160)/(8)\\m=20`

As we can see, no matter which points you use, it will always simplify to the same slope!

Now that we have the slope, we need to find the x and y intercepts! An x intercept is the point where y = 0 on the x-axis. A y intercept is the pint where x = 0 on the y-axis!

We already have a y intercept given to us, as you can see in the table there is a point (0, 23). This point is where x = 0! This will be our value next to the y in the equation. So so far, our equation looks like this:

`y-23=20(x-x_1)`

And how do we know what the x intercept (x1) is? Well, we have a table full of values, so we can use those to plug in for y and x! I want to note again, you do not need to worry about which values you use! Just make sure you have your x and y straight and plug in whichever pair of coordinates you want! I will use the point (-2, -17).

`(-17)-23=20((-2)-x_1)\\-40=20(-2-x_1)\\-2=-2-x_1\\x_1=0`

So it looks like this line goes straight through the origin! If you want to confirm your findings, you can just use another point. This time I'll just use (2, 63)!

`(63)-23=20(2-x_1)\\40=20(2-x_1)\\2=2-x_1\\x_1=0`

This also makes sense to be our x-intercept value since if it was any other number, our y intercept would not be (0, 23) and the given values wouldn't be true anymore! (This is just another way to confirm that it's right!)

Therefore, our final equation is:

y - 23 = 20 (x - 0)

y = 20x + 23 (same answer, just in a different form)