Point Slope Form

Front

What is the slope in the equation y=mx+b?

Back

The slope (m) represents the rate of change of y with respect to x.

Front

What does the y-intercept represent 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

How do you convert the point-slope form of a line to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the point-slope form of a line?

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.

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 equation of a line with a slope of 3 that passes through the point (2, 5)?

Back

Using point-slope form: y - 5 = 3(x - 2), which simplifies to y = 3x - 1.

Front

What is the significance of a slope of 0 in a linear equation?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about a line?

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 two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What is the slope of the line represented by the equation y = -4x + 7?

Back

The slope of the line is -4.