Question

Please answer and show all steps! Urgent :( Last 11 points I have left
Thank you!

Answer 1

Red Line: y =
`(5)/(2) x` - 9

Blue Line: y = -2x + 6

Yellow Line: y =
`(-1)/(3)x` + 9

Explanation:

y=mx+b is the slope-intercept formula for a line. This means that this equation tells you the y-intercept of a line as well as the slope of a line. In this formula, m is equal to the slope, and b is equal to the y-intercept.

The Y-intercept of a line is where the line crosses the y-axis.

The slope of a line is how much the line is increasing or decreasing by. You can calculate this number by dividing how much the line increases by the y-axis by how much the line increases on the x-axis. Essentially, you divide the line's rise over its run, or the change in y over the change in x.

Slope formula:
`(x_(1)-x_(2))/(y_(1)-y_(2))`

`x_(1)` and
`y_(1)` make up one coordinate, and
`x_(2)` and
`y_(2)` make up another. Both of these points must land on the same line--the line you are trying to find the slope of.

Red Line:

In this photo, we can clearly see what the y-intercept is. The slope intercept is -9, so b = -9.

To find the slope, you take two points and find the difference of their y-values and divide that by the difference of their x-values.

On the red line, we can see that the line crosses points (2, -4) and (0, -9). Let's find the slope by subtracting the y-values first:

-4 - (-9) = 5

5 is your change in y values, or your rise!

Now, let's subtract the x-values:

2 - 0 = 2

2 is your change in x values, or your run!

In order to finally find the slope of this line, you divide your change in y by your change in x. Therefore, you divide 5 by 2.

Your slope is
`(5)/(2)`. It's okay to leave slopes in fraction form!

So, now you plug in your slope and y-intercept that we found before into your formula! Remember:

b = y-intercept

m = slope

So, y =
`(5)/(2) x` - 9 is the formula for your line!

Red line: y =
`(5)/(2) x` - 9

Now, we repeat the process with the other lines. Let's do the blue line:

We can see that the y-intercept is 6. So, b = 6.

Now, let's calculate the slope. Let's find points on the blue line that we can use!

Point 1: (0, 6)

Point 2: (1, 4)

Let's subtract the y values:

6 - 4 = 2

Let's subtract the x values:

0 - 1 = -1

When we divide 2 (our change in y) by -1 (our change in x), we are left with -2 as our slope!

Slope = -2

So, when we plug everything into our equation, we get:

y = -2x + 6

Blue Line: y = -2x + 6

Now, for the last one!

We can see that the y-intercept is 9, so b = 9.

Let's calculate the slope:

Point 1: (0, 9)

Point 2: (3, 8)

Subtract the y-values:

9 - 8 = 1

Subtract the x-values:

0 - 3 = -3

Divide the change in y by the change in x:

1 ÷ -3 =
`(-1)/(3)`

Slope =
`(-1)/(3)`

Plug everything in!

y =
`(-1)/(3)x` + 9

Yellow Line: y =
`(-1)/(3)x` + 9