Learning Objectives
Introduction
Tutorial
The word 'intercept' looks like the word 'intersect'. Think of it as where the graph intersects the x-axis.
With that in mind, what value is y always going to be on the x-intercept? No matter where you are on the x-axis, y’s value is 0, that is a constant. We will use that bit of information to help us find the x-intercept.
y-interceptThis time it is x’s
value that is 0. Anywhere you would cross the y-axis, x’s
value is always 0. We will use this tidbit to help us find the y-intercept.
Below is an illustration of a graph of a linear function which highlights the x and y intercepts:
In the above illustration, the x-intercept
is the point (2, 0) and the y-intercept
is the point (0, 3).
Keep in mind that the x- and y- intercepts are two separate points. There is only one point that can be both an x- and y- intercept at the same time, do you know what point that is?
If you said the origin, (0, 0), give yourself a pat on the back.
A line going through
the point and having slope of m
would have the equation
When writing an equation of a line, keep in mind that you ALWAYS need two pieces of information when you go to write an equation:
Sometimes the directions will say to write the equation in the slope/intercept form. Basically this means to solve the equation for y. Note how y is by itself and everything else is on the other side. Most times you will need to start the problem using the point/slope form and then you just solve for y to get it into the slope/intercept form. Sometimes if you have it written in this form it makes it easier to work with when you graph.
Example 1: Write an equation for the line in point/slope form and slope/intercept form that has slope = -5 and passes through (2, 1).
Looks like we have all the information we need. We are ready to put our equation together.
Point/Slope Form:
*Slope/intercept form of the line
Example 2: Write an equation for the line in point/slope form and slope/intercept form that has slope = 3 and passes through the origin.
Do you know what the ordered pair for the origin is? If you said (0, 0) you are right on!!! That is the point that we will be using to plug into our equation.
Looks like we have all the information we need. We are ready to put our equation together.
Point/Slope Form:
Example 3: Write an equation for the line in point/slope form and slope/intercept form that passes through (-2, 1) and (2, 2).
We have more than enough points. However, what about the slope? Does this mean we can’t work out the problem? You are not going to get off that easily. We do have a way of finding the slope. Tutorial 25: The Slope of a Line shows us how we can get the slope given two points.
Let’s find that slope:
*Plug in values
*Simplify
Now it is just like examples 1 and 2 above, we want to put the slope and one point into the point/slope equation. Note that you can use either point to plug in as long as it is a point that the line passes through. I chose to plug in the point (-2, 1).
Point/Slope Form:
*Inverse of sub. 1 is add 1
*Slope/intercept form of the line
Example 4: Write an equation for the line in point/slope form and slope/intercept form that has an x-intercept of -2 and y-intercept of 1.
Do you know what the ordered pair is going to be for the x-intercept? What about the y-intercept?
Above, we leaned that an x-intercept is where the line crosses the x-axis. That means y’s value is always 0. So the ordered pair for our x-intercept is (-2. 0).
Above, we learned that an y-intercept is where the line crosses the y-axis.
That means x’s value is always 0.
So
the ordered pair for our y-intercept is
(0,
1).
We have more than enough points. However, what about the slope? Does this mean we can’t work out the problem? You are not going to get off that easily. We do have a way of finding the slope. Tutorial 25: The Slope of a Line shows us how we can get the slope given two points.
Let’s find that slope:
*Plug in values
*Simplify
Now it is just like examples 1 and 2 above, we want to put the slope and one point into the point/slope equation. Note that you can use either point to plug in as long as it is a point that the line passes through. I chose to plug in the point (-2, 0).
Point/Slope Form:
*Slope/intercept form of the line
Practice Problems
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1c: Write an equation for the line in point/slope form and slope/intercept form that has the given condition.
Need Extra Help on these Topics?
http://www.purplemath.com/modules/strtlneq.htm
This website helps you with writing linear equations.
Go to Get Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for some
more suggestions.
Last revised on Feb. 6, 2010 by Kim Seward.
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