2x-5y=8 4x+ky=17 For which of the following values of k will the system of equations above have no solution (A)-10 (B)-5 (C)0 (D)5 (E)10

When a system of linear equations has no solution, that means you have parallel lines, which means the lines have the same slope. So put both equations into slope-intercept form (y = mx + b) first: In order for those lines to be parallel, their slopes must be equal, which means 2/5 = -4/k. That means k must be (more…)

In the xy-plane what is the slope of the line that passes through the origin and makes a 42° angle with the positive x-axis? A. 0.67 B. 0.74 C. 0.90 D. 1.11

Trigonometry does the trick here. Below is that line making a 42° angle with the positive x-axis. I’ve also drawn a dotted segment to make myself a neat little right triangle. Remember that slope is rise over run—how high the line climbs divided by how far it travels right. In this case, the dotted segment (more…)

The figure above shows the graph of the function f(x)=ax +b, where a and b are constants. What is the slope of the graph of the function g(x)=-2f(x)

Note that f(x) is a line in slope-intercept form, where a is the slope and b is the intercept. Once you recognize that, you just need to know that, notationally, the –2 in front of f(x) means you multiply the whole thing by –2. So: That’s still a line, but now the slope is –2a. from Tumblr (more…)

The figure above shows the graph of the function f(x)=ax +b, where a and b are constants. What is the slope of the graph of the function g(x)=-2f(x)

Note that f(x) is a line in slope-intercept form, where a is the slope and b is the intercept. Once you recognize that, you just need to know that, notationally, the –2 in front of f(x) means you multiply the whole thing by –2. So: That’s still a line, but now the slope is –2a. from Tumblr (more…)

Test 5 Section 3 #13

Hi. Would it be possible for you to explain #13 on SAT practice test 5 on calculator inactive (the tea bag problem)? I think the main reason I found it confusing was the wording, and the SAT explanation for the answer was also a little bit wordy.
Thanks

The graph of a linear function f has a positive slope with intercepts (a,0) and (0,b)…

The graph of a linear function f has a positive slope with intercepts (a,0) and (0,b), where a and b are non-zero integers. Which of the following statements about a and b could be true?

A) a + b = 0

B) a – 2b = 0

C) a = b

D) 0 <a < b

(I only know that Choice C is out because that would be true only if the slope=1 and the line passed through the origin, but since a and b are non-zero integers, there can be no point (0,0), so that one answer choice is out. )