Final Alg 1 Review

Front

What is a solution of the inequality -2x + y ≤ -2?

Back

To determine if a point is a solution, substitute the x and y values into the inequality and check if the statement is true. For example, for the point (1, -1): -2(1) + (-1) ≤ -2 evaluates to -2 - 1 ≤ -2, which is true.

Front

Rewrite the equation -4x + 2y = 8 in slope-intercept form (y = mx + b).

Back

To isolate y, add 4x to both sides: 2y = 4x + 8. Then divide by 2: y = 2x + 4.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1). For points (2, -4) and (3, 1), m = (1 - (-4)) / (3 - 2) = 5.

Front

Solve the equation 7x − 2(x + 12) = −5 − 2(1 − 3x).

Back

First, simplify both sides: 7x - 2x - 24 = -5 - 2 + 6x. Combine like terms to get x = -17.

Front

What is the solution to the equation -3(1 + 2r) − (r + 1) = −10r + 7r?

Back

Distributing gives -3 - 6r - r - 1 = -3r. Combine like terms to find r = -1.

Front

What does slope-intercept form of a linear equation look like?

Back

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 2x + 4?

Back

The y-intercept is the value of y when x = 0. For y = 2(0) + 4, the y-intercept is 4.

Front

How do you determine if a point lies above or below a line represented by an inequality?

Back

Substitute the point's coordinates into the inequality. If the inequality holds true, the point lies on or above the line; if false, it lies below.

Front

What is the process to isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves. A positive slope rises, while a negative slope falls.