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Graphing Linear Equation y = 3x + 1 using Slope-Intercept Form
Published on March 11, 2026
Algebra
Graph the line defined by the equation y = 3x + 1 by identifying the y-intercept (b=1) and using the slope (m=3) to plot points.
Question
Answer
The user wants to graph the linear equation
This equation is in the slope-intercept form,
Step 1: Identify the y-intercept (
For the equation
For the equation
- The y-intercept is
. This means the line crosses the y-axis at the point . - The slope is
. This can be written as , meaning for every 1 unit moved to the right (rise over run), the line moves 3 units up.
Step 2: Plot the y-intercept.
Plot the point
Plot the point
Step 3: Use the slope to find a second point.
Starting from the y-intercept
Starting from the y-intercept
- Move right 1 unit (run = 1) to
. - Move up 3 units (rise = 3) to
.
This gives a second point.
We can find more points to ensure accuracy:
-
Starting from
, move left 1 unit (run = -1) to . -
Move down 3 units (rise = -3) to
.
This gives a third point. -
Starting from
, move left 2 units (run = -2) to . -
Move down 6 units (rise = -6) to
.
This gives a fourth point.
Step 4: Graph the line.
Draw a straight line passing through the points
Draw a straight line passing through the points
The graph of
The resulting graph should show a line connecting the points found above on the coordinate system provided.