Write Equations in 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 the formula: 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 a point-slope equation?

Back

In the point-slope form y - y1 = m(x - x1), the slope m is the coefficient of (x - x1).

Front

Write the point-slope form of the line that passes through (3, 1) with a slope of 2.

Back

y - 1 = 2(x - 3)

Front

What is the slope of the line represented by the equation y - 4 = 3(x - 2)?

Back

The slope of the line is 3.

Front

If a line passes through the point (6, 0) and has a slope of 1/3, what is its equation in point-slope form?

Back

y = \frac{1}{3}(x - 6) or y - 0 = \frac{1}{3}(x - 6) depending on the format.

Front

How do you convert the point-slope form 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

Write the point-slope form of the line that passes through (2, 4) and (3, 6).

Back

y - 4 = 2(x - 2) because the slope is 2.

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, which is used to determine the equation of the line.

Front

Write the point-slope form of the line that passes through (2, -2) with a slope of -4.

Back

y + 2 = -4(x - 2) or y = -4(x - 2) - 2.

Front

What does the slope represent in a linear equation?

Back

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