Linear Equations Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

Write the linear equation for the total cost (C) of buying x T-shirts at $15 each with a $5 shipping fee.

Back

C = 15x + 5

Front

Write the slope-intercept form of the equation for a line with a slope of 1/3 and passing through the origin.

Back

y = \frac{1}{3}x

Front

Write the equation that models a situation with a $20 startup fee and a $5 monthly fee.

Back

y = 5x + 20

Front

If a fitness club starts with 80 members and gains 15 members each month, what is the equation for total membership after x months?

Back

y = 15x + 80

Front

Write the equation for the total cost (C) of towing a vehicle for m miles with a flat fee of $50 and $8 per mile.

Back

C = 8m + 50

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

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

Back

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