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Course: Get ready for AP® Calculus>Unit 2

Lesson 2: Writing slope-intercept equations

Slope-intercept form review

Review slope-intercept form and how to use it to solve problems.

What is slope-intercept form?

Slope-intercept is a specific form of linear equations in two variables:
y, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #1fab54, b, end color #1fab54
When an equation is written in this form, start color #ed5fa6, m, end color #ed5fa6 gives the slope of the line and start color #1fab54, b, end color #1fab54 gives its y-intercept.

Finding slope-intercept equation from features or graph

Example 1: Equation from slope and intercept

Suppose we want to find the equation of the line whose slope is start color #ed5fa6, minus, 1, end color #ed5fa6 and y-intercept is left parenthesis, 0, comma, start color #1fab54, 5, end color #1fab54, right parenthesis. Well, we simply plug start color #ed5fa6, m, equals, minus, 1, end color #ed5fa6 and start color #1fab54, b, equals, 5, end color #1fab54 into slope-intercept form!
y, equals, start color #ed5fa6, minus, 1, end color #ed5fa6, x, start color #1fab54, plus, 5, end color #1fab54

Example 2: Equation from two points

Suppose we want to find the line that passes through the points left parenthesis, 0, comma, minus, 4, right parenthesis and left parenthesis, 3, comma, minus, 1, right parenthesis. First, we notice that left parenthesis, 0, comma, start color #1fab54, minus, 4, end color #1fab54, right parenthesis is the y-intercept. Second, we use the two points to find the slope:
\begin{aligned} \text{Slope}&=\dfrac{-1-(-4)}{3-0} \\\\\ &=\dfrac{3}{3} \\\\ &=\maroonC 1 \end{aligned}
Now we can write the equation in slope-intercept:
y, equals, start color #ed5fa6, 1, end color #ed5fa6, x, start color #1fab54, minus, 4, end color #1fab54
Problem 1
• Current
Write the equation of the line whose slope is 5 and y-intercept is left parenthesis, 0, comma, minus, 7, right parenthesis.
y, equals

Want to try more problems like this? Check out these exercises:

Finding features and graph from slope-intercept equation

When we have a linear equation in slope-intercept form, we can quickly find the slope and y-intercept of the corresponding line. This also allows us to graph it.
Consider, for example, the equation y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, start color #1fab54, plus, 3, end color #1fab54. We can quickly tell that the corresponding line has a slope of start color #ed5fa6, 2, end color #ed5fa6 and its y-intercept is left parenthesis, 0, comma, start color #1fab54, 3, end color #1fab54, right parenthesis. Now we can graph the line:
A coordinate plane. The x- and y-axes each scale by one. The equation y equals two x plus three is graphed and labeled. The points zero, three and one, five are plotted. There is a horizontal segment from zero, three to one, three that is labeled plus one. There is a vertical segment from one, three to one, five that is labeled plus two.
Problem 1
• Current
What is the slope of the line y, equals, 3, x, minus, 1?
What is the y-intercept of the line?
left parenthesis, 0, comma
right parenthesis

Want to try more problems like this? Check out these exercises:

Want to join the conversation?

• How do you an equation into slope intercept from slope and y intercept?
• It's quite easy.
Slope-intercept form: y = mx + b
The "m" is the slope. The "b" is the y-intercept.
So, if the problem tells you the slope = 3/4 and the y-intercept is -5, then you can create the equation by:
-- swap out "m" and put in 3/4
-- swap out "b" and put in -5
You get the equation: y = 3/4 (x) - 5
Hope this helps.
• I still don't know how to graph, this is so hard... :(
• y=mx+b

y=y
m=any number
x=x
b=any number
b is the y intercept, which is when x is zero what y is.
Did this help? Or do you not understand how to graph from a slope intercept form?
• This has no use in the real world.
• Slope? It can be used later to calculate really important things.
• I don't understand this.
• you said that two years ago i want to see if you will respond to my reply what grade are u in
• how do you find the slope
• Here's my explanation :)
The slope of the line is another way of saying How steep is this line?
To find an exact number for that, we use the concept rise over run.
First, you find two points on the line, (Let's say our points are (3,3) and (4,5))
Next you find out how much the line runs, aka how much it goes sideways within the two points we picked. To do that, you take the point with the greatest x value, and subtract the x value of the other point:
4-3=1
Now let's find the rise aka how much the line goes up within the two points we picked. To do that, we take the y value of our first point, and subtract the y value of our second point:
5-3=2
Now we have our Rise (2) and our Run (1), so let's put Rise over Run:
2/1
simplify
2
And we have the slope of the line!
• i dont know how to find slope
• pay attention to this review and write everything down the you will prob. get bro
• how can i graph lines without having the y intercept on the graph?
• You can graph any line from its equation by finding and graphing any 2 points that satisfy the equation.

Alternatively, if you know the slope and any point on the line you can graph the point and use the slope to find more points on the line.

You can find more details in the lessons at this link: https://www.khanacademy.org/math/algebra/two-var-linear-equations
• i don't understand how to put x intercept and y intercept in an equation
• You can put the equation into standard from (Ax+By=C) and then convert it into slope-intercept form (y=mx+b). I'm sure there are other ways to attack this problem, but this is how I learned it and it's quite efficient. Hope this helps!
• If the slope of a line, for example is 2/1, I understand that the slope is 2. But what do I do if the slope is something like 3/4 or 5/8?
(1 vote)
• It is quite common for slopes to be fractions.
A slope of 3/4 tells you that the line goes up 3 units as it moves right 4 units.
Similarly, a slope of 5/8 tells you that the line goes up 5 units as it moves 8 units to the right.

Hope this helps.
• how do I find the y intercept of the line with the equation 4x-5y+15=0? I'm so lost!
• The y-intercept is the point on the y-axis where the line crosses the y-axis. This means the x-coordinate for that point =0. Thus, you can always find the y-intercept by setting x=0 in the equation and solving for "y".
4(0) - 5y + 15 = 0
-5y + 15 = 0
15 = 5y
3 = y
Your y-intercept is at: (0, 3)
Hope this helps..