C)
D)
Here’s How to Crack It
Since the question asks for a line perpendicular to the line 2x + 5y = 10, you need to find the slope of the
line, and then take the negative reciprocal to find the slope. You could convert the equation into the y =
mx + b format in order to find the slope, or simply remember that when an equation is presented in the
form Ax + By = C, the slope is equal to – . So the slope of this line is – , and the slope of a
perpendicular line would be .
Look at the answer choices for one with a positive (upward) slope. Choices (B) and (C) slope
downward, so eliminate them. Next, use points in the graph to find the slope of each answer. Eliminate
(A); it has points at (1, 0) and (2, 5), for a slope of 5—too steep. The only remaining choice is (D), which
is the correct answer.
Two Equations with Infinitely Many Solutions
In the chapters on algebra, we talked about equations with one or multiple solutions. Now imagine an
equation in which any value of x would create a viable solution to the equation.
x + 3 = x + 3In this case, it is fairly obvious that any number you choose to put in for x will create a true equation. But
what does it mean when two lines have infinitely many solutions? Let’s look at an example.