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, meaning the value of y when x = 0.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line through the points (2, 3) and (5, 11)?

Back

The slope is m = (11 - 3) / (5 - 2) = 8 / 3.

Front

Does the line represented by the equation y = 2x + 5 pass through the origin?

Back

No, it does not pass through the origin because the y-intercept is 5.

Front

What does it mean if a line has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What is the slope of a horizontal line?

Back

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

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

How do you graph a line using the slope-intercept form?

Back

Start by plotting the y-intercept (b) on the y-axis, then use the slope (m) to find another point by rising and running.