Graphing Linear Equations

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

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

Front

What is the y-intercept of a line?

Back

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

Front

Convert the equation -3x + 4y = 12 to slope-intercept form.

Back

The slope-intercept form is y = 3/4x + 3.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the slope of the line that passes through the points (10, -8) and (1, 12)?

Back

The slope is -20/9.

Front

What is the equation of a line with a slope of -2 and a y-intercept of 4?

Back

The equation is y = -2x + 4.

Front

How do you graph a linear equation in 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 from the y-intercept.

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 in various contexts.