Graphing Slope-Intercept Form

Front

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

Back

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

Front

What does the slope (m) represent in the equation y = mx + b?

Back

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

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How do you find the y-intercept from the equation y = 3x?

Back

Set x = 0 in the equation. y = 3(0) = 0, so the y-intercept is (0, 0).

Front

How do you graph the equation y = -2x + 1?

Back

Start at the y-intercept (0, 1) and use the slope -2 to find another point: from (0, 1), go down 2 units and right 1 unit to (1, -1).

Front

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

Back

The slope is -1, indicating that for every 1 unit increase in x, y decreases by 1 unit.

Front

How can you determine if a line is increasing or decreasing from its slope?

Back

If the slope (m) is positive, the line is increasing. If the slope is negative, the line is decreasing.

Front

What is the graph of the equation y = 3x?

Back

The graph is a straight line that passes through the origin (0, 0) with a slope of 3, rising steeply.

Front

How do you convert the equation y = 1/3x - 2 into slope-intercept form?

Back

The equation is already in slope-intercept form, where the slope is 1/3 and the y-intercept is -2.

Front

What does it mean if a line has a slope of 0?

Back

A slope of 0 means the line is horizontal, indicating that y does not change as x changes.