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 from two points (x1, y1) and (x2, y2)?

Back

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

Front

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

Back

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

Front

What does the y-intercept represent in a linear equation?

Back

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

Front

If the slope of a line is negative, what does that indicate about the line's direction?

Back

A negative slope indicates that the line descends from left to right.

Front

If the slope of a line is positive, what does that indicate about the line's direction?

Back

A positive slope indicates that the line ascends from left to right.

Front

What is the slope of the line represented by the equation y = 4x + 3?

Back

The slope of the line is 4.

Front

Given m = 3 and b = 6, write the slope-intercept equation of the line.

Back

The slope-intercept equation is y = 3x + 6.

Front

How do you determine the y-intercept from the equation y = mx + b?

Back

The y-intercept can be determined directly from the equation as the value of 'b'.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 4)?

Back

The slope is (4 - 2) / (3 - 1) = 2 / 2 = 1.