Question

Help on theses as welll

Answer 1

Writing the Equation of a Line given the Graph

Answer:

15.
`y = \underline{16x}`

16.
`y = \underline{15x}`

Explanation:

We can write our line in Slope-Intercept form,
`y = mx +b`, where
`b` is the
`y`-intercept of the line which is the
`y`-coordinate when
`x = 0`and
`m` is the slope of the line which is calculated by
`(y_2 -y_1)/(x_2 -x_1)\\` where
`x_n` and
`y_n` is the
`xy`-coordinates of any point
`n` on the line.

For problem 15, we can see that at
`x = 0`,
`y = 0` as well. So
`b = 0`. To calculate the slope of the line, we choose any two points that is on line. We can see that points
`(0,0)` and
`(2,32)` is on the line so these are our points
`1` and
`2`.

Calculating the slope:

`m = (32 -0)/(2 -0) \\ m = (32)/(2) \\ m = 16`

Now we can plug everything we know and it is
`y = 16x +0` or
`y = 16x`.

We can apply the same procedure for problem 16. At
`x = 0`,
`y = 0` so
`b = 0`. For the slope, we can choose the points,
`(2,30)` and
`(4,60)`.

I'm not choosing
`(0,0)` (although choosing it will make it easier) just for kicks but the bottom line is, you can choose any point on the line you want.

Calculating the slope:

`m = (60 -30)/(4 -2) \\ m = (30)/(2) \\ m = 15`

The equation of the line can be written as
`y = 15x`.