Solving equations and inequalities for y

Front

What is the general form of a linear equation in two variables?

Back

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

Front

How do you solve for y in the equation 8x + 4y = 16?

Back

To solve for y, isolate y on one side: 4y = 16 - 8x, then y = -2x + 4.

Front

What does it mean to express y in terms of x?

Back

Expressing y in terms of x means rewriting the equation so that y is isolated on one side, showing how y depends on x.

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

How do you find the slope from the equation x + y = 4?

Back

Rearranging to slope-intercept form gives y = -x + 4, so the slope (m) is -1.

Front

What is the y-intercept in the equation y = -1/2x + 5?

Back

The y-intercept is the value of y when x = 0, which is 5 in this case.

Front

How do you graph the equation y = 5x - 16?

Back

Start at the y-intercept (0, -16) and use the slope (5) to find another point by going up 5 units and right 1 unit.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

How do you solve the inequality 3y - 9 > 18x?

Back

Add 9 to both sides: 3y > 18x + 9, then divide by 3: y > 6x + 3.

Front

What does the solution y > 6x + 3 represent graphically?

Back

It represents the region above the line y = 6x + 3 on a graph.