How do you find the slope and intercept of y = -5x + 2?

Aug 2, 2018

Slope: $- 5$

$x$-intercept: $\left(\frac{2}{5} , 0\right)$

$y$-intercept: $\left(0 , 2\right)$

Explanation:

$y = - 5 x + 2$

This equation is in slope-intercept form: Based on the image, we know that the slope is the value multiplied by $x$, so the slope is $- 5$.

To find the $x$-intercept, plug in $0$ for $y$ and solve for $x$:
$0 = - 5 x + 2$

Subtract $\textcolor{b l u e}{2}$ from both sides:
$0 \quad \textcolor{b l u e}{- \quad 2} = - 5 x + 2 \quad \textcolor{b l u e}{- \quad 2}$

$- 2 = - 5 x$

Divide both sides by $\textcolor{b l u e}{- 5}$:
$\frac{- 2}{\textcolor{b l u e}{- 5}} = \frac{- 5 x}{\textcolor{b l u e}{- 5}}$

$\frac{2}{5} = x$

$x = \frac{2}{5}$

The $x$-intercept is at $\left(\frac{2}{5} , 0\right)$.

To find the $y$-intercept, plug in $0$ for $x$ and solve for $y$:
$y = - 5 \left(0\right) + 2$

$y = 0 + 2$

$y = 2$

The $y$-intercept is at $\left(0 , 2\right)$.

Hope this helps!

Aug 2, 2018

Slope $- 5$, $x$-int $\frac{2}{5}$, $y$-int $2$

Explanation:

The good thing is that this equation is in slope-intercept form

$y = m x + b$, with slope $m$ and a $y$-intercept of $b$. With this in mind, we see that our slope is $- 5$ and our $y$-intercept is $2$.

What about the $x$-intercept?

The $x$-intercept is the value when $y = 0$. We can plug this into our equation to get

$0 = - 5 x + 2$

$- 5 x = - 2 \implies x = \frac{2}{5}$

Therefore, our slope is $- 5$, our $x$-intercept is $\frac{2}{5}$ and our $y$-intercept is $2$.

Hope this helps!