Linear Relationships Study Guide

Front

What is the formula to calculate the slope of a line?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is a proportional relationship?

Back

A proportional relationship is one where the ratio of y to x is constant, and the graph passes through the origin.

Front

If a line has a slope of 2.5, what does this indicate about the line's steepness?

Back

The line rises 2.5 units for every 1 unit it runs horizontally, indicating a steep upward slope.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

How can you determine if two triangles on a graph have the same slope?

Back

If the rise over run (change in y over change in x) is the same for both triangles, they have the same slope.

Front

What does it mean if a line is not proportional?

Back

It means that the line does not pass through the origin, indicating that there is a constant added to the output (y) value.

Front

Calculate the slope of the line passing through the points (1, 2) and (4, 8).

Back

Slope = (8 - 2) / (4 - 1) = 6 / 3 = 2.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.