Linear Relationships Study Guide

Front

What is the slope in a linear relationship?

Back

The slope is a measure of the steepness of a line, indicating how much the y-value changes for a unit change in the x-value.

Front

How do you find the slope from a table of values?

Back

Calculate the change in y divided by the change in x (rise/run) between two points.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

How do you write the equation of a line in slope-intercept form?

Back

Identify the slope (m) and y-intercept (b) from a graph or table, then write it as y = mx + b.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates.

Front

If a line has a slope of 4, what does this indicate?

Back

For every 1 unit increase in x, the y-value increases by 4 units.

Front

How can you determine the y-intercept from a graph?

Back

Locate the point where the line crosses the y-axis; this point's y-coordinate is the y-intercept.

Front

What is the y-intercept of the equation y = -2x + 4?

Back

The y-intercept is 4.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

Rearrange the equation to solve for y, isolating it on one side.