Let's first quickly review slope intercept form.
Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information. All you need to know is the slope (rate) and the y-intercept. Continue reading for a couple of examples!
Write the equation for a line that has a slope of -2 and y-intercept of 5.
NOTES: I substituted the value for the slope (-2) for m and the value for the y-intercept (5) for b. The variables x and y should always remain variables when writing a linear equation.
That's pretty easy, now let's look at a graph and write an equation based on the linear graph.
Write an equation for the following line:
NOTES: As I analyze the graph, I notice that the line crosses the y axis at the point, (0,-2). Therefore, my y-intercept is -2.
I then count the slope from the y-intercept to another point on the line. I count up 3 and right 1. 3/1, which means that my slope is 3. This is the value for m.
Just to double check that my slope is positive, I notice that as I follow the line from left to right, the line is rising. Therefore, my slope is positive.
The equation for this line is: y = 3x -2
Let's look at another graph.
Write an equation for the following line:
NOTES: As I analyze the graph, I notice that the y-intercept (y value of the point where the line crosses the y axis) is 3. So 3 is my value for b.
I then count the slope from the y-intercept to another point on the line. I count down 3 and right 4 (or I could count up 3 and left 4). Which means that my slope is -3/4. This is the value for m.
Just to double check that my slope is negative, I notice that as I follow the line from left to right, the line is falling. Therefore, my slope is negative.
The equation for this line is: y = -3/4x + 3
When you have a real world (word problem) that requires you to write an equation in slope intercept form, there are two things that you want to look for:
Use the chart below to help you organize your information as you analyze each word problem. This will help you when writing equations.
Take a look at the examples below to better clarify how this chart can help you.
And.... one more - just to make sure that writing equations is now EASY!
Writing Equations Unit
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