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Graphing a Line Given the Slope and y-Intercept
In this example, a linear function is graphed with zero slope and a zero y-intercept.
Review of the slope-intercept form:
In this set of Math Tutorials, we graph linear functions written in slope-intercept form, as shown below.
y = mx + b
In the slope-intercept form of a linear equation, the term m is the slope of the line and the term b is the y-intercept, where the line intersects the y-axis. In fact, if all you know about a linear equation is its slope and y-intercept, then you can write the equation in slope-intercept form.
Furthermore, you can graph the equation in slope-intercept form. Start by graphing the y-intercept, whose coordinates are (0, b). Next, express the slope m as a ratio of the rise over the run. From the y-intercept, move up the number of steps represented by the rise and move horizontally the number of steps represented by the run. If the the slope is negative, then you move horizontally to the left; otherwise, move horizontally to the right.
The new location is another point on the line. To complete the slope-intercept graph, connect the y-intercept to this point to construct the graph of the linear equation.
This set of Math Tutorials covers a variety of slope-intercept scenarios:
- Slope-intercept with negative slope, positive y-intercept
- Slope-intercept with negative slope, negative y-intercept
- Slope-intercept with negative slope, y-intercept at the origin
- Slope-intercept with positive slope, positive y-intercept
- Slope-intercept with positive slope, negative y-intercept
- Slope-intercept with positive slope, y-intercept at the origin
- Slope-intercept with zero slope, positive y-intercept
- Slope-intercept with zero slope, negative y-intercept
- Slope-intercept with zero slope, y-intercept at the origin
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The library of Math Tutorials is a comprehensive collection of worked-out solutions to common math problems. This overcomes a common limitation of most textbooks: the handful of worked-out examples for a given concept. We provide the full array of examples and solutions, allowing students to identify patterns among the solutions, in order to aid concept retention. We also have quizzes for many of these topics.
Our current inventory of Math Examples include:
- Math Tutorial: Examples Using Algebra Tiles
- Math Tutorial: Solving Equations in One Variable
- Math Tutorial: Solving Equations with Fractions
- Math Tutorial: Solving Equations with Percents
- Math Tutorial: Slope formula
- Math Tutorial: Midpoint formula
- Math Tutorial: Distance formula
- Math Tutorial: Graphing linear functions, given m and b
- Math Tutorial: Graphing absolute value functions
- Math Tutorial: Graphing linear inequalities
- Math Tutorial: Using the Point-Slope form
- Math Tutorial: Finding the equation of a line given two points
- Math Tutorial: Graphing parallel and perpendicular lines
- Math Tutorial: Solving quadratics graphically
- Math Tutorial: Solving quadratics by completing the square
- Math Tutorial: Factoring Quadratics
