Linear Equations: Word Problems and Beyond

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 value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How do you interpret the y-intercept in a real-world context?

Back

The y-intercept often represents a fixed starting value in a real-world scenario, such as an initial fee or starting quantity.

Front

What is the equation for a fitness club membership that starts with 80 members and increases by 15 each month?

Back

y = 15x + 80

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points, calculate the slope (m) using (y2 - y1) / (x2 - x1), then use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What does the term 'initial fee' mean in a word problem?

Back

The initial fee is a fixed cost that must be paid before any additional costs are incurred, often represented as the y-intercept in a linear equation.

Front

How can you determine the equation of a line from a table of values?

Back

Identify the pattern in the changes of y with respect to x to find the slope, then use one of the points to find the y-intercept.

Front

What is the equation for the height of a tree that grows from 7' to 15' over 8 years?

Back

h = t + 5, where h is the height and t is the number of years.

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.