How to graph lines in slope-intercept form?
Understand the Problem
The question is asking how to graph lines that are represented in slope-intercept form, which typically is expressed as y = mx + b, where m is the slope and b is the y-intercept. The process involves identifying these values and then plotting the line accordingly on a graph.
Answer
Graphing a line involves plotting the y-intercept and using the slope to find additional points on the line.
Answer for screen readers
To graph a line in slope-intercept form, identify the slope and y-intercept, plot the y-intercept, use the slope to find another point, and then draw the line through those points.
Steps to Solve
- Identify the slope (m) and y-intercept (b)
From the slope-intercept form $y = mx + b$, identify the slope $m$ and the y-intercept $b$ of the given line.
- Plot the y-intercept on the graph
Start by plotting the point at the y-coordinate equal to $b$. This is the point where the line crosses the y-axis. For example, if $b = 2$, you would plot the point (0, 2).
- Use the slope to find another point
The slope $m$ tells you how to move from the y-intercept to find another point on the line. If the slope is $\frac{rise}{run}$, calculate the "rise" (vertical change) and "run" (horizontal change). For example, if $m = 3$, it means a rise of 3 units up for every 1 unit you run to the right.
- Plot the second point using the slope
From the y-intercept point you plotted, move according to the slope to find a new point. For our example, from (0, 2), move up 3 and right 1 to the point (1, 5).
- Draw the line
Connect the two points with a straight line using a ruler or drawing tool. Extend the line in both directions and add arrows to indicate that the line continues indefinitely.
To graph a line in slope-intercept form, identify the slope and y-intercept, plot the y-intercept, use the slope to find another point, and then draw the line through those points.
More Information
Graphing lines in slope-intercept form is a fundamental skill in algebra. Understanding how to interpret the slope and y-intercept allows you to graph any linear equation easily.
Tips
- Confusing slope and y-intercept: Make sure you accurately identify which value is the slope and which is the y-intercept.
- Improperly calculating the slope: Remember that the slope is represented as a fraction $\frac{rise}{run}$. Ensure to move in the correct direction.
