Point-Slope and Slope-Intercept Equations

Front

What is the Point-Slope form of a linear equation?

Back

The Point-Slope form is given by the equation: y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

How do you convert Point-Slope form to Slope-Intercept form?

Back

To convert from Point-Slope form (y - y_1 = m(x - x_1)) to Slope-Intercept form (y = mx + b), solve for y.

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 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

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

Back

The slope of the line is -3.

Front

How do you find the y-intercept from the Slope-Intercept form?

Back

The y-intercept is the value of y when x = 0, which is represented by b in the equation y = mx + b.

Front

What is the equation of a line with a slope of 2 that passes through the point (1, 3) in Point-Slope form?

Back

The equation is y - 3 = 2(x - 1).

Front

If a line has a slope of -1/2, what does this indicate about its direction?

Back

A slope of -1/2 indicates that for every 2 units the line moves to the right, it moves down 1 unit.

Front

What is the significance of the coordinates in the Point-Slope form equation?

Back

The coordinates (x_1, y_1) represent a specific point through which the line passes.

Front

How do you determine the coordinates of a point from the Point-Slope form equation?

Back

You can determine the coordinates by rearranging the equation to find x and y values.