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 the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

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 y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How can you determine if a linear equation is in slope-intercept form?

Back

A linear equation is in slope-intercept form if it is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the equation y = 2/3x - 3 represent?

Back

This equation represents a line with a slope of 2/3 and a y-intercept of -3.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, then use the slope to find another point and draw a straight line through the points.

Front

What is the relationship between x and y in the equation y = 5x + 5?

Back

In this equation, for every increase of 1 in x, y increases by 5. The slope is 5 and the y-intercept is 5.

Front

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

Back

The equation is y = 15x + 80, where y is the total membership and x is the number of months.

Front

What does a negative slope indicate about a line?

Back

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