A.2C 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 (m) represent in a linear equation?

Back

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

Front

What does the y-intercept (b) represent in a linear equation?

Back

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

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-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 the two points.

Front

What is the difference between a 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

What is a vertical line and how is it represented?

Back

A vertical line has an undefined slope and is represented by the equation x = a, where a is the x-coordinate of any point on the line.

Front

What is a horizontal line and how is it represented?

Back

A horizontal line has a slope of 0 and is represented by the equation y = b, where b is the y-coordinate of any point on the line.

Front

How do you interpret the equation y = 25x + 40 in a real-world context?

Back

This equation represents a situation where for every hour (x) worked, $25 is earned, plus a fixed service fee of $40.