Slope and Y-intercept Word Problems

Front

What is the slope in a linear equation?

Back

The slope is the rate of change of the y-value with respect to the x-value, often represented as 'm' in the equation y = mx + b.

Front

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

Back

The y-intercept is the value of y when x is 0, represented as 'b' in the equation y = mx + b.

Front

Write the equation for a line with a slope of 2 and a y-intercept of 5.

Back

y = 2x + 5

Front

If a river's water level is receding at a rate of 0.5 feet per day, what is the slope of the equation representing this situation?

Back

The slope is -0.5, indicating a decrease in water level.

Front

How do you write an equation for a situation where a cost includes a flat fee and a variable cost per hour?

Back

The equation is C = flat fee + (variable cost per hour * hours).

Front

What is the equation for a plumber who charges $25 for a service call plus $50 per hour?

Back

C = 25 + 50h, where C is the total cost and h is the number of hours.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept and use the slope to find another point, then draw a line through these points.

Front

What is the equation for a canoe rental service that charges a $20 transportation fee and $30 per hour?

Back

y = 30x + 20, where y is the total cost and x is the number of hours.

Front

If a babysitter charges a flat fee of $3 plus $5 per hour, what is the equation representing this situation?

Back

C = 3 + 5h, where C is the total cost and h is the number of hours.

Front

What does the term 'linear relationship' mean?

Back

A linear relationship means that there is a constant rate of change between two variables, represented by a straight line on a graph.