Slope
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces slope as a measure of the steepness of a line. Students learn to calculate slope as rise over run (change in y divided by change in x) between any two points on a line, and interpret positive, negative, zero, and undefined slopes.
Key Concepts
Property The Greek letter $\Delta$ ('delta') is used in mathematics to indicate change. The slope of a line is defined by the ratio $$ \frac{\text{change in } y\text{ coordinate}}{\text{change in } x\text{ coordinate}} $$ as we move from one point to another on the line. In symbols, the slope, denoted by $m$, is: $$ m = \frac{\Delta y}{\Delta x} $$.
Examples For a line passing through points $(2, 5)$ and $(4, 9)$, the change in $y$ is $\Delta y = 9 5 = 4$ and the change in $x$ is $\Delta x = 4 2 = 2$. The slope is $m = \frac{4}{2} = 2$.
If we move from point $A(1, 3)$ to point $B(5, 6)$, the slope is $m = \frac{\Delta y}{\Delta x} = \frac{6 3}{5 1} = \frac{3}{4}$.
Common Questions
What is slope in algebra?
Slope measures the steepness and direction of a line. It is calculated as rise over run: slope = (change in y) / (change in x) = (y2 - y1) / (x2 - x1).
How do you calculate slope from two points?
Use the formula m = (y2 - y1) / (x2 - x1). For example, for points (1, 2) and (3, 6): m = (6-2)/(3-1) = 4/2 = 2.
What does a positive slope mean?
A positive slope means the line rises from left to right. A negative slope means it falls from left to right. Zero slope is a horizontal line.
What is undefined slope?
A vertical line has undefined slope because the change in x is zero, making the denominator zero in the slope formula.
Where is slope introduced in Grade 6?
Slope is introduced in the Yoshiwara Elementary Algebra textbook for Grade 6 as a foundational concept for linear equations.