Graphing Slope-Intercept Equations
| Site: | Saylor Academy |
| Course: | GKT101: General Knowledge for Teachers – Math |
| Book: | Graphing Slope-Intercept Equations |
| Printed by: | Guest user |
| Date: | Tuesday, 20 May 2025, 8:11 AM |
Description
As you have seen from examples, you can write linear equations in different ways. There are three main forms of linear equations: slope-intercept, point-slope, and standard. This lecture series introduces the point-slope form. Watch the videos and complete the interactive exercises. This lecture series focuses on graphing linear equations when they are given in slope-intercept form.
Graph from slope-intercept equation
Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations#x2f8bb11595b61c86:graphing-slope-intercept-equations
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
Graph from slope-intercept form - Questions
1. Graph \(y=-x-6\).
2. Graph \(y=\frac{2}{3} x-4\)
3.Graph \(y=-3 x+7\).
4. Graph \(y=\frac{6}{5} x+1\).
Answers
1. The equation is in slope-intercept form: \(y=m \cdot x+b\). In this form, \(m\) gives us the slope of the line and \(b\) gives us its \(y\)-intercept.
So \(y=-x-6\) has a slope of \(-1\) and a \(y\)-intercept at \( (0,-6)\).
We need two points. We already have the \(y\)-intercept \((0,-6)\).
We can find a second point by reasoning about the slope. A slope of \(-1\) means when the \(x\)-value increases by \(1\), the \(y\)-value decreases by \(1\).
\((0+1,-6-1)=(1,-7)\)
Now we can graph the equation.
2. The equation is in slope-intercept form: \(y=m \cdot x+b\). In this form, \(m\) gives us the slope of the line and \(b\) gives us its \(y\)-intercept.
So \(y=\frac{2}{3} x-4\) has a slope of \(\frac {2}{3}\) and a \(y\)-intercept of \((0. -4)\).
We need two points. We already have the \(y\)-intercept \((0,-4)\).
We can find a second point by reasoning about the slope. A slope of \(\frac{2}{3}\) means that when the \(x\)-value increases by \(3\), the \(y\)-value increases by \(2\).\((0+3,-4+2)=(3,-2)\)
Now we can graph the equation.
3. The equation is in slope-intercept form: \(y=m \cdot x+b\). In this form, \(m\) gives us the slope of the line and \(b\) gives us its \(y\)-intercept.
So \(y = -3x+7\) has a slope of \(-3\) and a \(y\)-intercept at \((0,7)\).
We need two points. We already have the \(y\)-intercept \((0,7)\).
We can find a second point by reasoning about the slope. A slope of \(-3\) means that when the \(x\)-value increases by \(1\), the \(y\)-value decreases by \(3\).
\((0+1,7-3)=(1,4)\)
Now we can graph the equation.
4. The equation is in slope-intercept form: \(y=m \cdot x+b\). In this form, \(m\) gives us the slope of the line and \(b\) gives us its \(y\)-intercept.
So \(y=\frac{6}{5} x+1\) has a slope of \(\frac{6}{5}\) and a \(y\)-intercept at \((1, 0)\).
We need two points. We already have the \(y\)-intercept \((0,1)\).
We can find a second point by reasoning about the slope. A slope of \(\frac {6}{5}\) means that when the \(x\)-value increases by \(5\), the \(y\)-value increases by \(6\).
\((0+5,1+6)=(5,7)\)
Now we can graph the equation.
