Point-Slope Form

Front

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

Back

The point-slope form of a linear equation 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 identify the slope from the point-slope form equation y + 1 = -3(x - 5)?

Back

The slope is the coefficient of (x - x1), which in this case is -3.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

If a line has a slope of -3, what does this indicate about its direction?

Back

A slope of -3 indicates that the line descends from left to right.

Front

How can you determine if a point lies on a line given in point-slope form?

Back

Substitute the x and y coordinates of the point into the equation. If the equation holds true, the point lies on the line.

Front

What is the slope of the line that passes through the points (6, 7) and (4, 2)?

Back

The slope is 5/2.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the point (x1, y1) in the point-slope form?

Back

The point (x1, y1) is a specific point on the line used to define the line's position.

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert, solve for y: y = mx + (y1 - mx1).

Front

What is the slope of the line represented by the equation y + 5 = -3(x - 6)?

Back

The slope is -3.