Point Slope Form of a Line

Front

What is the point-slope form of a line?

Back

The point-slope form of a line 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 from 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 does the slope (m) represent in the point-slope form?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the slope of the line represented by the equation y + 5 = 2(x - 3)?

Back

The slope of the line is 2.

Front

If a line has a slope of -3 and passes through the point (1, 4), what is its point-slope form?

Back

The point-slope form is y - 4 = -3(x - 1).

Front

What is the significance of the point (x_1, y_1) in the point-slope form?

Back

The point (x_1, y_1) is a specific point on the line that helps define its position.

Front

How do you find the slope between two points (x_1, y_1) and (x_2, y_2)?

Back

The slope (m) is calculated using the formula: m = (y_2 - y_1) / (x_2 - x_1).

Front

Convert the equation y + 2 = 5(x - 4) into slope-intercept form.

Back

The slope-intercept form is y = 5x - 22.

Front

What is the point-slope form of a line that passes through (3, -5) with a slope of 2?

Back

The point-slope form is y + 5 = 2(x - 3).

Front

If the equation of a line is y - 1 = 3(x + 2), what is the slope?

Back

The slope is 3.