Question

Write an equation of the line in standard form?

The line has the same slope as 6x-y = 5 and the same​ y-intercept as the graph of 4y-9x = 8.
What is the equation in standard form?

Answer 1

`y-6x=2`

Explanation:

Formulas of lines have the form `y=ax+b`.

• The slope is `a`. For example, `y=5x` means that the y-coordinate increases by 5 for every `x`.
• The y-intercept is `b`. For example, `y=5x+2` has a y-intercept at the coordinates `(0,2)`.

First, write the given equations in the form `y=ax+b`.

`6x-y=5`

Subtract 6x from both sides.

`-y=5-6x`

Multiply both sides by -1.

`y=6x-5`

`4y-9x=8`

Add 9x to both sides.

`4y=9x+8`

Divide both sides by 4.

`y=2 1/4x+2`

In the first equation, `a=6` (the slope is 6). In the second equation, `b=2` (the y-intercept is 2).

Fill in the slope and the y-intercept into the `y=ax+b` form, and you've got the line `y=6x+2` or `y-6x=2` in standard form.

Answer 2

The equation of the new line in standard form is `y-6x=2`.

Explanation:

`6x-y=5` is a linear equation in standard form: `Ax+Bx=C`. We can find the slope by converting it to slope-intercept form: `y=mx+b`, where `m` is the slope. To convert the equation to slope-intercept form, solve for `y`.

`6x-y=5`

Subtract `6x` from both sides.

`-y=-6x+5`

Divide both sides by `-1`. This will reverse the signs.

`y=6x-5`

`m=6`

`4y-9x=8` is also in standard form. We can find the y-intercept by converting to the slope-intercept form, `y=mx+b`, where `b` is the y-intercept. Solve for `y` to convert to the slope-intercept form.

`4y-9x=8`

Add `9x` to both sides.

`4y=9x+8`

Divide both sides by `4`.

`y=9/4x+8/4`

Simplify `8/4` to `2`.

`y=9/4x+2`

`b=2`

The new equation where `m=6` and `y=2` can be written in slope-intercept form and then converted to standard form.

The new equation is:

`y=6x+2`

To convert to standard form, subtract `6x` from both sides.

`y-6x=2`