Foundations Final Exam Review

Front

What is the equation of a line that is perpendicular to the graph of 4x + 3y = 9?

Back

The slope of the line 4x + 3y = 9 is -\frac{4}{3}. The slope of a perpendicular line is \frac{3}{4}. The equation can be found using point-slope form.

Front

What is the solution to the equation -2 = \frac{r+4}{8}?

Back

The solution is r = -20.

Front

Is (0,0) a solution to the system of equations represented by solid lines?

Back

Yes, because the point is on a solid line in the solution section.

Front

What is the slope of the line represented by the equation 2y = -5x + 10?

Back

The slope is -\frac{5}{2}.

Front

What point does the line y + 5 = -3(x - 2) contain?

Back

The point is (2, -5).

Front

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

Back

The slope m is calculated as m = \frac{y2 - y1}{x2 - x1}.

Front

What does it mean for a line to be perpendicular to another line?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

Front

What is the y-intercept of the line represented by the equation 2y = -5x + 10?

Back

The y-intercept is 5.