1st Semester Review

Front

Graph the system and identify how many solutions it has: y = -2x + 2 and y = 4x - 4.

Back

To graph the system, plot both lines on the same coordinate plane. The number of solutions corresponds to the number of intersection points: 0 (parallel lines), 1 (intersecting lines), or infinitely many (coincident lines).

Front

Evaluate f(x) = 10x + 3x^2 at x = -3.

Back

f(-3) = 10(-3) + 3(-3)^2 = -30 + 27 = -3.

Front

What is the slope of a line perpendicular to the graph of y = 2x + 5?

Back

The slope of the given line is 2. The slope of a line perpendicular to it is the negative reciprocal: -1/2.

Front

If f(x) = -3x - 5, find f(-1).

Back

f(-1) = -3(-1) - 5 = 3 - 5 = -2.

Front

Solve the system of equations by substitution: y = 6x and 2x + 3y = -20.

Back

Substituting y in the second equation: 2x + 3(6x) = -20 leads to 20x = -20, so x = -1. Then, y = 6(-1) = -6. The solution is (-1, -6).

Front

What is the definition of a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

Define slope in the context of a graph.

Back

Slope is a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the y-intercept of the line y = 3x + 4?

Back

The y-intercept is the point where the line crosses the y-axis, which is (0, 4) for this equation.

Front

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

Back

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