Graph Slope of a Line

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented as (0, b) in the equation of the line y = mx + b.

Front

Write the equation of a line with a slope of -3 and y-intercept of 8.

Back

y = -3x + 8

Front

Determine the slope and y-intercept from the equation: y = \frac{3}{2}x + 3.

Back

slope: \frac{3}{2}, y-intercept: (0, 3)

Front

How does the graph of y = -2x + 4 compare with the graph of y = -2x?

Back

It is parallel to y = -2x but 4 units higher.

Front

Find the equation that represents the line going through (0, 2) and (-4, 0).

Back

y = \frac{1}{2}x + 2

Front

What effect does multiplying x by a constant \alpha have on the graph of y = x?

Back

The graph becomes steeper or less steep.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = \frac{y2 - y1}{x2 - x1}.

Front

What does a positive slope indicate about a line?

Back

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

Front

What does a negative slope indicate about a line?

Back

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