Slope of a line
Calculate the slope of a line in Grade 9 algebra using rise over run. Apply the slope formula (y₂-y₁)/(x₂-x₁) and classify lines as positive, negative, zero, or undefined.
Key Concepts
Property The slope of a line is a rate of change. It is equal to the ratio of the vertical change (rise) to the horizontal change (run). $$ \operatorname{slope} = \frac{\operatorname{rise}}{\operatorname{run}} $$.
Examples A line rises 8 units for every 2 units it runs to the right: $\operatorname{slope} = \frac{8}{2} = 4$. A line falls 9 units for every 3 units it runs to the right: $\operatorname{slope} = \frac{ 9}{3} = 3$. A line passes through (1, 2) and (5, 10): $\operatorname{slope} = \frac{10 2}{5 1} = \frac{8}{4} = 2$.
Explanation Slope is just a fancy word for how steep a line is on a graph. It is the ultimate measure of its tilt! We call the vertical change the 'rise' (like climbing a ladder) and the horizontal change the 'run' (like running across a field). A big slope means a super steep hill, while a small slope is a gentle walk.
Common Questions
What is the formula for slope of a line?
Slope = (y₂ - y₁)/(x₂ - x₁), also written as rise/run. It measures how steeply a line rises or falls moving from left to right.
What do positive, negative, zero, and undefined slopes mean?
Positive slope rises left to right, negative slope falls, zero slope is horizontal, and undefined slope is vertical (division by zero in the formula).
How do you find slope from a graph?
Pick two points on the line, count the vertical change (rise) and horizontal change (run) between them, then divide rise by run. Always move from left to right.