Slope and Y-Intercept from Graphs

Front

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

Back

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

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is. It is calculated as the rise over run (change in y divided by change in x).

Front

How do you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, calculate the vertical change (rise) and the horizontal change (run) between these points, and then divide rise by run.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The y-intercept can be found by locating the point where the line crosses the y-axis.

Front

If a line has a slope of 2, what does this indicate about the line?

Back

A slope of 2 indicates that for every 1 unit increase in x, the value of y increases by 2 units.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

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

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to isolate all terms on one side.

Front

What is the slope of the line represented by the equation y = -3x + 2?

Back

The slope of the line is -3.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.