Slope-intercept form
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the slope-intercept form of a linear equation: y = mx + b. Students learn that m represents the slope (rate of change) and b represents the y-intercept (starting value), and use this form to graph lines and write linear equations.
Key Concepts
Property A linear equation written in the form $$y = mx + b$$ is said to be in slope intercept form. The coefficient $m$ is the slope of the graph, and $b$ is the $y$ intercept.
Examples The equation $y = 3x + 5$ is in slope intercept form. The slope is $3$ and the $y$ intercept is $(0, 5)$. For $y = 2x 1$, the slope is $ 2$ and the $y$ intercept is $(0, 1)$. In the equation $y = \frac{1}{2}x + 4$, the slope is $\frac{1}{2}$ and the $y$ intercept is $(0, 4)$.
Explanation This form is a recipe for drawing a line. The '$b$' tells you your starting point on the y axis, and the '$m$' (slope) gives you directions on how steep to draw the line from there.
Common Questions
What is slope-intercept form?
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept—the value of y when x equals zero.
How do you graph a line in slope-intercept form?
Start by plotting the y-intercept (0, b) on the y-axis. Then use the slope m = rise/run to move from that point and plot the next point, then draw the line.
How do you write an equation in slope-intercept form?
Identify the slope m and y-intercept b, then substitute into y = mx + b.
What does the y-intercept tell you about a line?
The y-intercept is where the line crosses the y-axis (x = 0). It represents the starting value in many real-world contexts.
Where is slope-intercept form taught in Grade 6?
Slope-intercept form is introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.