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

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 does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

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

Back

The slope is -1.

Front

What is the y-intercept of the equation y = 3x - 4?

Back

The y-intercept is -4.

Front

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

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 equation of a line that passes through the points (1, 2) and (3, 6)?

Back

The equation is y = 2x.

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 do you convert the equation 2x + 3y = 6 into slope-intercept form?

Back

Rearranging gives y = -2/3x + 2.