# What is the equation of the line which is parallel to the line 3x +4y =6 and passes through (2, 1)?

## Show work and explain please.

Dec 1, 2017

$y = - \frac{3}{4} x + \frac{5}{2}$

#### Explanation:

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$3 x + 4 y = 6$

Let's solve for $y$ so we can have the equation in standard slope-intercept form:

$4 y = - 3 x + 6$

$y = - \frac{3}{4} x + \frac{3}{2}$

This is in the form of:

$y = m x + b$ where $m$ is slope and $b$ is the $y$-intercept which is where the line crosses the $y$-axis. Comparing the two we see that:

$m = - \frac{3}{4}$ and $b = \frac{3}{2}$

For a line to be parallel to this line, it would have to have the same slope, i.e. its equation would be:

$y = - \frac{3}{4} x + b$

Now, we can use the coordinates of the point the line goes through and plug them into this equation to solve for $b$:

$1 = - \frac{3}{4} \left(2\right) + b$

$1 = - \frac{3}{2} + b$

$b = 1 + \frac{3}{2} = \frac{2}{2} + \frac{3}{2} = \frac{5}{2}$

Therefore, the equation of the line is:

$y = - \frac{3}{4} x + \frac{5}{2}$