Forms of Linear Equations

Front

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

Back

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

Front

How do you identify the slope and y-intercept in the equation y = 3x + 6?

Back

In the equation y = 3x + 6, the slope (m) is 3 and the y-intercept (b) is 6.

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

What is the standard form of a linear equation?

Back

The standard form of a linear equation is given by Ax + By = C, where A, B, and C are constants.

Front

How do you convert the slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side.

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

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How can you find the slope from two points (x₁, y₁) and (x₂, y₂)?

Back

The slope (m) can be calculated using the formula m = (y₂ - y₁) / (x₂ - x₁).

Front

What is the formula to write the equation of a line given a point and a slope?

Back

The equation of a line can be written using the point-slope form: y - y₁ = m(x - x₁).

Front

How do you write the equation of a line in point-slope form that passes through (4, -7) with a slope of -1/4?

Back

Using the point-slope form: y + 7 = -1/4(x - 4).