This page assumes you have some basic knowledge of linear equations and slope. In the linear equations basics section we discussed the standard form of a linear equation where Ax + By = C.
There are other ways that linear equations can be written that can help provide useful information for graphing. They are called slope forms. There is the slope-intercept form and the point-slope form.
Slope-Intercept Form
The slope intercept form uses the following equation:
In this equation, x and y are still the variables. The coefficients are m and b. These are numbers.
The advantage of putting a linear equation in this form is that the number for m equals the slope and the number for b equals the y-intercept. This makes the line the equation represents simple to graph.
m = slope
b = intercept
slope = (change in y) divided by the (change in x) = (y2 - y1)/(x2 - x1)
intercept = the point where the line crosses (or intercepts) the y-axis
Example Problems:
1) Graph the equation y = 1/2x + 1
From the equation y = mx + b we know that:
m = slope = ½
b = intercept = 1
1) Graph the equation y = 3x - 3
From the equation y = mx + b we know that:
m = slope = 3
b = intercept = -3
Point-Slope Form
The point-slope form of linear equation is used when you know the coordinates of one point on the line and the slope. The equation looks like this:
y1, x1 = the coordinates of the point you know
m = the slope, which you know
x, y = variables
Example Problems:
Graph a line that passes through the coordinate (2,2) and has a slope of 3/2. Write the equation in the slope-intercept form.
See the graph below. First we plotted the point (2,2) on the graph. Then we found another point using a rise of 3 and a run of 2. We drew a line between these two points.
To write this equation in slope-intercept form we use the equation:
y = mx + b
We already know that the slope (m) = 3/2 from the question. The y-intercept (b) we can see is at -1 from the graph. We can fill in m and b to get the answer:
y = 3/2x -1
Things to Remember
There are other ways that linear equations can be written that can help provide useful information for graphing. They are called slope forms. There is the slope-intercept form and the point-slope form.
Slope-Intercept Form
The slope intercept form uses the following equation:
y = mx + b
In this equation, x and y are still the variables. The coefficients are m and b. These are numbers.
The advantage of putting a linear equation in this form is that the number for m equals the slope and the number for b equals the y-intercept. This makes the line the equation represents simple to graph.
m = slope
b = intercept
slope = (change in y) divided by the (change in x) = (y2 - y1)/(x2 - x1)
intercept = the point where the line crosses (or intercepts) the y-axis
1) Graph the equation y = 1/2x + 1
From the equation y = mx + b we know that:
m = slope = ½
b = intercept = 1
From the equation y = mx + b we know that:
m = slope = 3
b = intercept = -3
Point-Slope Form
The point-slope form of linear equation is used when you know the coordinates of one point on the line and the slope. The equation looks like this:
y - y1 = m(x - x1)
y1, x1 = the coordinates of the point you know
m = the slope, which you know
x, y = variables
Example Problems:
Graph a line that passes through the coordinate (2,2) and has a slope of 3/2. Write the equation in the slope-intercept form.
See the graph below. First we plotted the point (2,2) on the graph. Then we found another point using a rise of 3 and a run of 2. We drew a line between these two points.
To write this equation in slope-intercept form we use the equation:
y = mx + b
We already know that the slope (m) = 3/2 from the question. The y-intercept (b) we can see is at -1 from the graph. We can fill in m and b to get the answer:
y = 3/2x -1
- Slope-intercept form is y = mx + b.
- Point-slope form is y - y1 = m(x - x1).
- We can write a linear equation in three different ways: standard form, slope-intercept form, and point-slope form.