slope and graphing linear equations

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

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 y when x = 0.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that the line descends from left to right, meaning for every 1 unit increase in x, y decreases by 2 units.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where 'a' is a constant.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where 'b' is a constant.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = (-A/B)x + (C/B).

Front

What is the slope of the line represented by the equation y = 3x + 5?

Back

The slope of the line is 3.

Front

What is the slope of the line represented by the equation y = -rac{1}{2}x + 4?

Back

The slope of the line is -rac{1}{2}.