Writing Linear Equations

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 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

What does 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the fixed costs (y-intercept), and the variable costs (slope), then formulate the equation in the form y = mx + b.

Front

What is the slope of the equation y = 0.95x + 7.95?

Back

The slope of the equation y = 0.95x + 7.95 is 0.95.

Front

What is the y-intercept of the equation y = 30 + 12.5x?

Back

The y-intercept of the equation y = 30 + 12.5x is 30.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y to 0 in the equation and solve for x.

Front

What is the x-intercept of the equation y = -30x + 100?

Back

To find the x-intercept, set y to 0: 0 = -30x + 100, which gives x = 100/30 = 10/3.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as x increases, y decreases, meaning the line descends from left to right.

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept represents the starting value or fixed cost in a real-world scenario, such as the initial fee before any variable costs are added.