# How do you graph y=1/4x -5?

Jun 18, 2017

See below

#### Explanation:

You can solve this by making a table of values. However, I will solve this more mathematically (sorta).

The $- 5$ part says that the $y$-intercept of this line is $- 5$. The $y$-intercept is the point at which a line crosses the $y$ axis. Therefore, $x$ is always $0$ for the $y$ intercept.

The $\frac{1}{4} x$ is implying that the slope or the gradient (same thing) of this line is $\frac{1}{4}$. Therefore, $\frac{R i s e}{R u n} = \frac{1}{4}$. $\frac{R i s e}{R u n}$ can be expanded to $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

Since we already know that the point $\left\{0 , - 5\right\}$ lies on this line, let's substitute ${x}_{2}$ for $0$ and ${y}_{2}$ for $- 5$.

$\frac{- 5 - {y}_{1}}{0 - {x}_{1}} = \frac{1}{4}$

Now, if you choose a point for ${x}_{1}$, you can simply work out ${y}_{1}$. For example, let's say I chose $4$.

$\frac{- 5 - {y}_{1}}{0 - 4} = \frac{1}{4}$

$= \frac{- 5 - {y}_{1}}{-} 4 = \frac{1}{4}$

Now, what makes $\frac{1}{4}$ when divided by $- 4$? The answer is $- 1$.

Therefore, we need $- 1$ on the numerator. We already have $- 5$, and ${y}_{1}$ is negative, so the number $- 4$ fits. So the coordinates for the 2nd point is $\left\{4 , - 4\right\}$

$\frac{- 5 - - 4}{-} 4 = \frac{1}{4}$

$= \frac{- 1}{-} 4 = \frac{1}{4}$

Now, with the points we have, $\left\{0 , - 5\right\}$ and $\left\{4 , - 4\right\}$, we can graph this by plotting the points and joining them.

You should get this graph{y=1/4x-5 [-10, 10, -5, 5]}

Sorry for this long answer, but with enough practice, you really don't need to go through all of the steps. You develop a muscle memory so that you sort of know what you need to do.