# How do you find the slope and intercept of  5-x = y/3?

Apr 4, 2016

The slope is 3 and the y-intercept is -15.

#### Explanation:

To solve this problem, we must first put the original equation in slope-intercept form. To do this, we'll multiply each side by 3 to get $15 - 3 x = y$, or $y = 3 x - 15$. From here, it's easy to find the slope and intercept. Since slope-intercept form is $y = m x + b$, where m is the slope and b is the y-intercept, the slope is 3 and the y-intercept is -15.

Apr 4, 2016

$\textcolor{b l u e}{{x}_{\text{intercept}} = 5}$

$\textcolor{b l u e}{{y}_{\text{intercept}} = 15}$

$\textcolor{b l u e}{\text{The slope is } - 3}$

#### Explanation:

Given:$\text{ } 5 - x = \frac{y}{3}$

Multiply both sides by 3

$3 \left(5 - x\right) = y \times \frac{3}{3}$

But $\frac{3}{3} = 1$

$y = 3 \left(5 - x\right)$

Multiply everything inside the brackets by 3

$y = 15 - 3 x$

The slope is the number (coefficient) in front of the $x$

$\textcolor{b l u e}{\text{So the slope is } - 3}$

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This means that as you read from left to right: for every 1 along you go down by 3. If the slope had been +3 that would mean you go up by 3 for every 1 along.
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$\textcolor{b l u e}{\text{To determine y-intercept}}$

The ${y}_{\text{intercept}}$ is the constant of 15 from $y = - 3 x + 15$

$\textcolor{b l u e}{{y}_{\text{intercept}} = 15}$
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$\textcolor{b l u e}{\text{To determine x-intercept}}$

$\textcolor{b r o w n}{\text{Calculation shown in a lot of detail}}$
$\textcolor{b r o w n}{\text{Normally a lot od steps would be skipped}}$

The ${x}_{\text{intercept}}$ is when y=0

$0 = - 3 x + 15$

Subtract 15 from both sides

$- 15 = - 3 x + 0$

divide both sides by 3

$- \frac{15}{3} = x \times - \frac{3}{3}$

$- 5 = - x$

Multiply everything by (-1)

$5 = x$

$x = 5$

$\textcolor{b l u e}{{x}_{\text{intercept}} = 5}$