Lines Have Constant Slope
Lines have constant slope is a Grade 7 math concept from Yoshiwara Intermediate Algebra establishing that the slope between any two points on the same line is always the same. This property is what makes linear functions consistent and predictable, and it is the defining characteristic distinguishing lines from curves.
Key Concepts
Property The slope of a line is constant: no matter which two points you pick to compute the slope, you will always get the same value.
Because $m$ is constant for a given line, we can use the formula $m = \frac{\Delta y}{\Delta x}$ to find $\Delta y$ when we know $\Delta x$, or to find $\Delta x$ when we know $\Delta y$.
We can also tell whether a collection of data points lies on a straight line by computing slopes between them.
Common Questions
Why do lines have constant slope?
A line is defined as having equal rise-to-run ratio between any two points on it. If the ratio changed, the graph would curve, making it nonlinear.
How do you verify slope is constant using multiple points?
Pick any two pairs of points on the line and calculate the slope for each pair. If all slopes are equal, the line has constant slope.
What does constant slope tell you about a linear function?
Constant slope means the function changes at a fixed rate — a hallmark of proportional or linear relationships.
Is it possible for a nonlinear curve to have a constant slope?
No. If a curve has a constant slope at every point, it must be a straight line.