Linear Equations Review

Front

What is the formula for the slope between two points \( (x_1,y_1) \) and \( (x_2,y_2) \)?

Back

The formula for the slope \( m \) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Front

What is the slope-intercept form for a line?

Back

The slope-intercept form of a line is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Front

Rewrite the equation \( 6x - 2y = -14 \) in slope-intercept form.

Back

The slope-intercept form is \( y = 3x + 7 \).

Front

Rewrite the equation \( 10x + 4y = 0 \) in slope-intercept form.

Back

The slope-intercept form is \( y = -\frac{5}{2}x \).

Front

Find the slope of the line that passes through the points (4,-7) and (2,-7).

Back

The slope \( m = 0 \) because the y-coordinates are the same.

Front

What does it mean if the slope of a line is zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

What is the significance of the y-intercept in the slope-intercept form?

Back

The y-intercept is the point where the line crosses the y-axis, represented by \( b \) in the equation \( y = mx + b \).

Front

How do you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Front

How do you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero.