# 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?

May 28, 2018

$y - 6 x = 2$

#### Explanation:

Formulas of lines have the form $y = a x + b$.

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

First, write the given equations in the form $y = a x + b$.

$6 x - y = 5$

Subtract 6x from both sides.

$- y = 5 - 6 x$

Multiply both sides by -1.

$y = 6 x - 5$

$4 y - 9 x = 8$

$4 y = 9 x + 8$

Divide both sides by 4.

$y = 2 \frac{1}{4} x + 2$

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 $y = a x + b$ form, and you've got the line $y = 6 x + 2$ or $y - 6 x = 2$ in standard form.

May 28, 2018

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

#### Explanation:

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

$6 x - y = 5$

Subtract $6 x$ from both sides.

$- y = - 6 x + 5$

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

$y = 6 x - 5$

$m = 6$

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

$4 y - 9 x = 8$

Add $9 x$ to both sides.

$4 y = 9 x + 8$

Divide both sides by $4$.

$y = \frac{9}{4} x + \frac{8}{4}$

Simplify $\frac{8}{4}$ to $2$.

$y = \frac{9}{4} x + 2$

$b = 2$

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:

$y = 6 x + 2$

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

$y - 6 x = 2$