Slope-Intercept Form Examples

Graph the equation y = -½x – 2.

The slope of the line is -½, which means that it slopes downhill and isn't very steep. We also know that it crosses the y-axis at -2. We'll start by plotting the y-intercept and then counting over to the next point using a slope of -½.

Remember that slope equals rise over run, so this line moves downward by 1 in the vertical direction for every 2 in the horizontal. Also, since it's a negative slope, make sure that our line moves downhill from left to right.

Graph the equation 4x + y = 7.

Unfortunately, this equation is not given to us in slope-intercept form ☹. However, we can solve the equation for y and manipulate it into this form.

	subtract 4x from each side
	simplify
	switch the 7 and 4x, but keep the appropriate signs

Now we can see that the slope of this equation is , also known as  when written as a fraction, and the y-intercept is .

Graph the equation 2y = x.

Again, we need to solve for y, since it's not in y = mx + b form.

	divide each side by 2
	simplify
or y =

Now we can see that the slope of the equation is ½, but where is b, the y-intercept? Can't find it? That's because it's just 0; it's not necessary to write y = ½x + 0.

Let's plot a y-intercept of 0 and use the slope of ½ to find a few other points.

Find the equation of the line in slope-intercept form.

Let's look carefully at the graph and see if we can find any important information….

Right off the bat, we can see that the y-intercept is 1. We can also find the slope by counting the change in the vertical and horizontal directions between the two points shown.

From the point (0, 1) to (3, 2), our line is has a "rise" of 1 and a "run" of 3. Slope is rise over run, so that gives us a slope of ⅓.

Now using that information, we know these things:

b = 1 and m = ⅓

All we need to do is plug them into our equation, y = mx + b.

y = ⅓x + 1