Graph using the slope-intercept method
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to graph linear equations using the slope-intercept method. Students identify the slope and y-intercept from the equation y = mx + b, plot the y-intercept first, then use the slope to find additional points and draw the line.
Key Concepts
Property To Graph a Line Using the Slope Intercept Method: 1. Write the equation in the form $y = mx + b$. 2. Plot the $y$ intercept, $(0, b)$. 3. Write the slope as a fraction, $m = \frac{\Delta y}{\Delta x}$. 4. Use the slope to find a second point on the graph: Starting at the $y$ intercept, move $\Delta y$ units in the $y$ direction, then $\Delta x$ units in the $x$ direction. 5. Find a third point by moving $ \Delta y$ units in the $y$ direction, then $ \Delta x$ units in the $x$ direction, starting from the $y$ intercept. 6. Draw a line through the three plotted points.
Examples To graph $y = \frac{2}{3}x + 1$, first plot the $y$ intercept at $(0, 1)$. From there, use the slope to move up 2 units and right 3 units to find a second point at $(3, 3)$. For $y = 3x + 5$, start by plotting $(0, 5)$. Write the slope as $\frac{ 3}{1}$, then move down 3 units and right 1 unit to find the point $(1, 2)$. To graph $y = \frac{5}{2}x 3$, plot the intercept at $(0, 3)$. From that point, move up 5 units and right 2 units to locate a second point at $(2, 2)$.
Explanation This method is like a treasure map for graphing. Start at 'X marks the spot' on the y axis (the intercept, $b$), then follow the slope's 'rise over run' directions to find your next point and draw the line.
Common Questions
What is the slope-intercept method for graphing?
Identify the y-intercept b and slope m from y = mx + b. Plot the point (0, b), then use rise over run to move to the next point, and draw the line through both points.
How do you find the slope and y-intercept from y = mx + b?
The coefficient of x is the slope m, and the constant b is the y-intercept. For y = 2x + 3, slope = 2 and y-intercept = 3.
What does rise over run mean when graphing?
Rise over run is how you move from one point to the next using the slope. A slope of 2/3 means move up 2 units and right 3 units.
Can you graph a line with a negative slope using this method?
Yes. A negative slope means move down (negative rise) and right. For slope -1/2, move down 1 unit and right 2 units.
Where is graphing using slope-intercept method taught?
The slope-intercept graphing method is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.