7.5 Graphing equations in slope-intercept form

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

1. The $y\text{-intercept}$ is the point $\left(0,2\right)$ . Thus the line crosses the $y\text{-axis}$ 2 units above the origin. Mark a point at $\left(0,2\right)$ .
   
   
2. The slope, $m$ , is $\frac{3}{4}$ . This means that if we start at any point on the line and move our pencil $3$ units up and then $4$ units to the right, we’ll be back on the line. Start at a known point, the $y\text{-intercept}\left(0,2\right)$ . Move up $3$ units, then move $4$ units to the right. Mark a point at this location. (Note also that $\frac{3}{4}=\frac{-3}{-4}$ . This means that if we start at any point on the line and move our pencil $3$ units down and $4$ units to the left , we’ll be back on the line. Note also that $\frac{3}{4}=\frac{\frac{3}{4}}{1}$ . This means that if we start at any point on the line and move to the right $1$ unit, we’ll have to move up $3/4$ unit to get back on the line.)
   
   
3. Draw a line through both points.
   
   

$y=-\frac{1}{2}x+\frac{7}{2}$

1. The $y\text{-intercept}$ is the point $\left(0,\frac{7}{2}\right)$ . Thus the line crosses the $y\text{-axis}$ $\frac{7}{2}\text{units}$ above the origin. Mark a point at $\left(0,\frac{7}{2}\right)$ , or $\left(0,3\frac{1}{2}\right)$ .
   
   
2. The slope, $m$ , is $-\frac{1}{2}$ . We can write $-\frac{1}{2}$ as $\frac{-1}{2}$ . Thus, we start at a known point, the $y\text{-intercept}$ $\left(0,3\frac{1}{2}\right)$ , move down one unit (because of the $-1$ ), then move right $2$ units. Mark a point at this location.
   
   
3. Draw a line through both points.
   
   

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

1. We can put this equation into explicit slope-intercept by writing it as $y=\frac{2}{5}x+0$ .
   
   The $y\text{-intercept}$ is the point $\left(0,0\right)$ , the origin. This line goes right through the origin.
   
   
2. The slope, $m$ , is $\frac{2}{5}$ . Starting at the origin, we move up $2$ units, then move to the right $5$ units. Mark a point at this location.
   
   
3. Draw a line through the two points.

$y=2x-4$

1. The $y\text{-intercept}$ is the point $\left(0,-4\right)$ . Thus the line crosses the $y\text{-axis}4$ units below the origin. Mark a point at $\left(0,-4\right)$ .
   
   
2. The slope, $m$ , is 2. If we write the slope as a fraction, $2=\frac{2}{1}$ , we can read how to make the changes. Start at the known point $\left(0,-4\right)$ , move up $2$ units, then move right $1$ unit. Mark a point at this location.
   
   
3. Draw a line through the two points.