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 convert 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

What does the slope (m) represent in a linear equation?

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 that passes through the points (2, 3) and (4, 7)?

Back

The slope is m = (y₂ - y₁) / (x₂ - x₁) = (7 - 3) / (4 - 2) = 2.

Front

Write the equation in point-slope form for the line with slope 3 that passes through the point (1, 2).

Back

y - 2 = 3(x - 1).

Front

What is the slope-intercept form of the line with slope -2 and y-intercept 5?

Back

The slope-intercept form is y = -2x + 5.

Front

How do you find the y-intercept from the point-slope form?

Back

To find the y-intercept from point-slope form, set x = 0 and solve for y.

Front

What is the y-intercept of the line given by the equation y = 1/2x - 4?

Back

The y-intercept is -4.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal.

Front

What is the equation of a vertical line that passes through the point (3, 4)?

Back

The equation of the vertical line is x = 3.