REWRITING LINEAR EQUATIONS

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

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that the line is increasing from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing from left to right.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Convert the equation 2x + 3y = 6 to slope-intercept form.

Back

y = -2/3x + 2.

Front

What is the significance of the slope in a real-world context?

Back

The slope represents the rate of change, such as speed or cost per item.

Front

How can you determine if a line is horizontal?

Back

A line is horizontal if its slope is 0, meaning it does not rise or fall.

Front

How can you determine if a line is vertical?

Back

A line is vertical if its slope is undefined, meaning it goes straight up and down.

Front

What is the formula for the point-slope form of a linear equation?

Back

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.