SAT Math: Heart of Algebra

Front

What is the solution to the equation x/32 = 3/8?

Back

x = 12

Front

How do you find the equation of a line given two points, (-1, -5) and (1, 3)?

Back

Use the slope formula: m = (y2 - y1) / (x2 - x1) to find the slope, then use point-slope form to find the equation. The equation is y = 4x - 1.

Front

If a sandwich has 3.5 times as many calories as a deluxe chocolate brownie, and the total calories for 2 sandwiches and 3 brownies is 2100, how do you find the calories in one brownie?

Back

Let b be the calories in one brownie. Then, 2(3.5b) + 3b = 2100. Solve for b to find b = 210.

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²). For points (-1, -4) and (4, 8), the distance is 13.

Front

What happens to the function y = 2x when it is shifted vertically 7 units upward?

Back

The resulting function is y = 2x + 7.

Front

Define the term 'slope' in the context of a linear equation.

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on a line.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers.

Front

How do you convert the slope-intercept form of a line (y = mx + b) to standard form?

Back

Rearrange the equation to get Ax + By = C, where A, B, and C are integers.

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, represented by the value of b in the slope-intercept form y = mx + b.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts.