Graphing Lines in 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, represented as (0, b).

Front

How do you find the y-intercept from the equation y = -3x + 4?

Back

The y-intercept is 4, which means the line crosses the y-axis at the point (0, 4).

Front

What is the slope of the line represented by the equation y = -2x + 1?

Back

The slope of the line is -2, indicating that for every 1 unit increase in x, y decreases by 2 units.

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 = 1/3x - 2?

Back

The graph is a straight line with a slope of 1/3 and a y-intercept of -2.

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

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

Back

The x-intercept is the point where the line crosses the x-axis, found by setting y = 0 in the equation.

Front

How do you find the x-intercept from the equation y = -3x + 4?

Back

Set y = 0: 0 = -3x + 4, solving gives x = 4/3, so the x-intercept is (4/3, 0).