1st Semester Algebra Review

What is the definition of a linear equation?

• An equation that forms a straight line when graphed, typically in the form y = mx + b.

• An equation that represents a curve on a graph.

• An equation that has no solutions.

• An equation that can only be solved using complex numbers.

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

• Use the formula: slope = (y2 - y1) / (x2 - x1).

• Calculate the average of the y-coordinates.

• Subtract the x-coordinates and divide by the sum of the y-coordinates.

• Use the formula: slope = (x2 - x1) / (y2 - y1).

What is the y-intercept of a line?

• The point where the line crosses the x-axis, represented as (a, 0) in the equation y = mx + b.

• The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

• The slope of the line, represented as m in the equation y = mx + b.

• The distance from the origin to the line, measured along the y-axis.

What does it mean if a system of equations has infinitely many solutions?

• The lines representing the equations are parallel and never intersect.

• The lines representing the equations coincide, meaning they are the same line.

• The lines representing the equations intersect at exactly one point.

• The lines representing the equations have different slopes.

How do you determine if a relation is a function from a set of ordered pairs?

• Check if any x-value is repeated; if it is, the relation is not a function.

• Verify that all y-values are unique for each x-value.

• Ensure that the relation contains at least one ordered pair.

• Count the total number of ordered pairs in the relation.

What does the graph of x > 2 look like?

• A line on the x-axis starting from 2 and extending to the right, not including 2.

• A line on the x-axis starting from 2 and extending to the left, including 2.

• A vertical line at x = 2, including all points on the line.

• A shaded area to the left of x = 2, including 2.

What is a function?

• A relation where each input has exactly one output.

• A set of numbers that can be added together.

• A method for solving equations with multiple variables.

• A graphical representation of data points.

What is the slope of the line through the points (6, -2) and (3, 7)?

• @@rac{9}{-3} = -3@@

• @@rac{5}{-3} = -rac{5}{3}@@

• @@rac{9}{3} = 3@@

• @@rac{-9}{3} = -3@@

What does the graph of x ≤ -3 look like?

• A line on the x-axis starting from -3 and extending to the left, including -3.

• A line on the x-axis starting from -3 and extending to the right, including -3.

• A vertical line at x = -3 extending upwards and downwards.

• A dashed line at x = -3, indicating that -3 is not included.

What does it mean if a system of equations has no solution?

• The lines representing the equations are parallel and never intersect.

• The lines intersect at one point.

• The lines coincide and represent the same equation.

• The lines intersect at multiple points.