Graphing 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

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 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 of the line represented by the equation y = -2x + 4?

Back

The slope of the line is -2.

Front

What is the y-intercept of the line represented by the equation y = ⅔x - 1?

Back

The y-intercept of the line is -1.

Front

How do you graph the equation y = x - 4?

Back

To graph y = x - 4, start at the y-intercept (0, -4) and use the slope of 1 to find another point (1, -3). Draw a line through these points.

Front

What is the equation of a line with a slope of 4/3 and a y-intercept of 4?

Back

The equation is y = 4/3x + 4.

Front

How do you write the equation of a line given a slope and a y-intercept?

Back

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

Front

What is the slope of the line represented by the equation y = 2/3x - 3?

Back

The slope of the line is 2/3.