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?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the y-intercept of 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

Write the equation of a line with a slope of 3 that passes through the point (0, 2).

Back

y = 3x + 2.

Front

What is the difference between positive and negative slope?

Back

A positive slope means the line rises as it moves from left to right, while a negative slope means the line falls as it moves from left to right.

Front

How do you write a linear equation in slope-intercept form?

Back

To write a linear equation in slope-intercept form, use the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if a line has a slope of zero?

Back

A line with a slope of zero is horizontal, meaning there is no change in y as x changes. The equation is of the form y = b.

Front

What is the equation of a line with a slope of -1 that passes through the point (2, 3)?

Back

y = -1(x - 2) + 3, which simplifies to y = -x + 5.

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.