# How do you draw the line with the slope m=1/2 and y- intercept 5?

Apr 15, 2017

Start at the y-intercept and count $\text{rise"/"run}$ for the slope.

#### Explanation:

The equation of the line is $y = \frac{1}{2} x + 5$

You know that the $y$-intercept is at $5$. This is the point where the line crosses the $y$-axis.

Slope is defined as $\text{y-change"/"x-change" = "vertical"/"horizontal}$

Slope = $\frac{1}{2}$ means $2$ y units for each $1$ x unit.

Starting from the y-intercept at 5:
count UP 1 unit and RIGHT 2 units, mark a point. $\left(2 , 6\right)$
Repeat this process, marking marking points up and to the right.

Starting from the y-intercept at 5:
count DOWN 1 unit and LEFT 2 units, mark a point. $\left(- 2 , 4\right)$
Repeat this process, marking marking points down and to the left.

Join the points with a straight line.

graph{1/2x+5 [-19.73, 20.27, -7.08, 12.92]}

Apr 15, 2017

$y = \frac{1}{2} x + 5$

#### Explanation:

Standard form of an equation of a line is $y = m x + b$ where $m$ = slope = $\frac{{y}_{2} - {y}_{1}}{{m}_{2} - {m}_{1}}$ and $b$ is the $y$-intercept, which is the point $\left(0 , b\right)$

Start by plotting the $y$-intercept $\left(0 , 5\right)$

The slope $m = \frac{1}{2}$. From the $y$-intercept $\left(0 , 5\right)$, go up $1 , \left(+ y\right)$ and over $2 , \left(+ x\right)$ and place a point. Draw a line that passes through the two points.

graph{y = 1/2x + 5 [-9.29, 10.71, 1.32, 11.32]}