Graphing Linear Equations

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

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, indicating how steep the line is.

Front

What is the y-intercept in the equation y = -3x + 7?

Back

The y-intercept is the point where the line crosses the y-axis, which is (0, 7) in this case.

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept (b) in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0, indicating where the line crosses the y-axis.

Front

Given a slope of 2/3 and a y-intercept of (0, -3), what is the equation of the line?

Back

The equation is y = (2/3)x - 3.

Front

What does a positive slope indicate about a linear graph?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a linear graph?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

How can you determine if a point (x, y) lies on the line represented by the equation y = mx + b?

Back

Substitute the x-value into the equation and see if the resulting y-value matches the y-coordinate of the point.

Front

What is the graphical representation of the equation y = 2x + 3?

Back

The graph is a straight line with a slope of 2 and a y-intercept at (0, 3).