Question

These two lines are parallel. Write an equation for each.

Answer 1

Top: y = x

Bottom: y = 0.8x - 3.2

Explanation:

I can see the question is asking to write the equation in Slope-Intercept form.

Slope-Intercept Form:

y = mx+b

M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.

Because these lines are parallel, we know they have the same form.

Lets look at the top line. When x increases by one, how much does y increase by?

1

What is the y value of when the line's x-value is 0?

0

Now, we have,

y = 1x + 0

Because adding 0 keeps the equation the same, we can remove it.

y = 1x

Because multiplying a term by 1 leaves it the same, we can remove one.

y = x

Now, for the bottom line.

How much does y increase by when x increases by 1? Because the slope will be a fraction and is not easy to see, I will use the slope formula.

Slope Formula:

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

To find the slope, take any pair of points on the line and plug them in.

I'll use:

(0,-3.2)

(4,0)

Plug the y-values (the latter number, or the height of the point) into the formula. Do the same with the x-values. keep in mind it does not matter what y-value you plug in. For example, for
`y_2` and
`y_1` you can plug in -3.2 and 0 or vice versa. If you make
`y_2` -3.2, then make
`x_(2)` 0.

`(-3.2-0)/(0-4)`

Simplify.

`(-3.2)/(-4)`

Because a negative number multiplied or divided by another negative number is always a positive number, remove the negative signs.

`(3.2)/(4)`

Divide.

3.2/4 = 0.8

Now we have m, the slope on the 2nd line, 0.8

y = 0.8x + b

What is the y-value of the line when the line has the x-value of 0? On the graph, it says -3.2.

y = 0.8x - 3.2