Writing Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line, typically 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 y with respect to x, indicating how much y changes for a unit change in x.

Front

What is the y-intercept of a linear equation?

Back

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

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a linear equation is increasing or decreasing?

Back

If the slope (m) is positive, the line is increasing; if the slope is negative, the line is decreasing.

Front

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

Back

It represents a situation where there are 120 gallons of water in a tank that releases water at a rate of 25 gallons per minute.

Front

What does the y-intercept of the equation y = 3x + 10 represent in a gym membership context?

Back

It represents the monthly fee that Rich pays for his gym membership, regardless of the number of visits.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to get y = (-A/B)x + (C/B).

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept indicates the starting value of y when x is zero, providing insight into the initial condition of the situation being modeled.