Point Slope Word Problems

Front

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

Back

The point-slope form is given by y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

Front

How do you identify the slope from a point-slope equation?

Back

The slope is the coefficient of (x - x₁) in the point-slope form equation.

Front

What does the term 'rate of change' refer to in a linear context?

Back

The rate of change refers to how much the dependent variable (y) changes for a unit change in the independent variable (x). It is represented by the slope (m) in a linear equation.

Front

Given the equation y - 3 = 2(x + 4), what is the slope?

Back

The slope is 2.

Front

What point does the line y - 3 = 2(x + 4) pass through?

Back

The line passes through the point (-4, 3).

Front

If a climber's altitude changes from 400 feet to 700 feet over 4 hours, what is the average rate of change?

Back

The average rate of change is 75 feet per hour.

Front

Write the point-slope equation for a line with a slope of 75 that passes through the point (6, 700).

Back

The point-slope equation is y - 700 = 75(x - 6).

Front

What is the significance of the point (0, 10) in the context of Mrs. Taylor's height?

Back

It indicates that at 0 seconds, Mrs. Taylor was 10 feet off the ground.

Front

Write a point-slope equation for Mrs. Taylor's height at 5 seconds if she is 20 feet off the ground.

Back

The point-slope equation is y - 20 = 2(x - 5).

Front

How do you find the rate of change from two points?

Back

The rate of change is calculated by (change in y) / (change in x) between the two points.