Linear Equations Review 2023

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 convert the equation y - 5 = (1/3)(x - 18) to slope-intercept form?

Back

To convert to slope-intercept form, distribute (1/3) to (x - 18) and then isolate y: y = (1/3)x - 1.

Front

What is the y-intercept of the equation 3x + y = 5?

Back

The y-intercept is the point (0, 5).

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What does the slope of a line represent?

Back

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

Front

How do you convert the equation y - 3 = -2(x + 4) to slope-intercept form?

Back

Distribute -2 to (x + 4) and isolate y: y = -2x - 5.

Front

What is the significance of the slope in the equation y = 4x + 5?

Back

In this equation, the slope is 4, indicating that for every unit increase in x, y increases by 4 units.

Front

What is the general form of a linear equation?

Back

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

Front

How can you determine if two lines are parallel using their equations?

Back

Two lines are parallel if they have the same slope (m) in their slope-intercept forms.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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