Three Forms of Linear Equations

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 find the y-intercept of a linear equation in standard form?

Back

To find the y-intercept of a linear equation in standard form Ax + By = C, set x = 0 and solve for y.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

Convert the equation 3x + 4y = 24 to slope-intercept form.

Back

The slope-intercept form is y = -3/4x + 6.

Front

What does the slope of a line represent?

Back

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

Front

Given the points (2, 3) and (4, 7), what is the slope of the line connecting them?

Back

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

Front

What is the y-intercept of the line represented by the equation y = 2x + 5?

Back

The y-intercept is 5.

Front

Write the equation of a line in point-slope form given a slope of 1/2 and the point (2, 3).

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A ≥ 0.

Front

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

Back

To convert from point-slope form y - y₁ = m(x - x₁) to slope-intercept form, solve for y.