Linear Functions: Slope Intercept Form

Front

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

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope in the equation y = mx + b?

Back

In the equation y = mx + b, the slope (m) represents the rate of change of y with respect to x.

Front

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

Back

The y-intercept (b) represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

How can you determine the equation of a line from a word problem?

Back

To determine the equation of a line from a word problem, identify the slope and y-intercept from the context of the problem and use the slope-intercept form.

Front

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

Back

The slope indicates how much one quantity changes in relation to another, often representing rates such as speed, cost per item, or production rate.

Front

If a line has a negative slope, what does that indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How do you convert a word problem into a linear equation?

Back

Identify key quantities, determine the rate of change (slope), and the starting value (y-intercept) to formulate the linear equation.

Front

What does the equation y = -25x + 120 represent in a real-world scenario?

Back

This equation represents a situation where there are initially 120 gallons of water in a tank, and it releases water at a rate of 25 gallons per minute.

Front

In the equation y = 3x + 8, what do the numbers 3 and 8 represent?

Back

In this equation, 3 is the slope (tacos made per minute), and 8 is the y-intercept (initial number of tacos made).

Front

How can you find the y-intercept from a linear equation?

Back

The y-intercept can be found by setting x to 0 in the equation and solving for y.