Slope Word Problems and Graphs

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing an upward trend.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing a downward trend.

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 (0, b) in the equation y = mx + b.

Front

How can you identify the slope and y-intercept from the equation of a line in slope-intercept form?

Back

In the equation y = mx + b, m represents the slope and b represents the y-intercept.

Front

What is the slope of the line represented by the equation y = 2x + 5?

Back

The slope (m) is 2.

Front

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

Back

The y-intercept (b) is 4.

Front

How do you write the equation of a line given a slope and a point on the line?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the equation of a line that has a slope of 1 and passes through the point (2, 3)?

Back

The equation is y - 3 = 1(x - 2), which simplifies to y = x + 1.