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…)

# In the system of equations above, a and b represent the cost, in dollars, of buying x buffalo wings at two different restaurants…

In the system of equations above, a and b represent the cost, in dollars, of buying x buffalo wings at two different restaurants. What amount of money will get you the same number of buffalo wings at both restaurants?

# Test 5 Section 4 #11

Can you work out problem #11 of section four in Official SAT #5?

# 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

# Test 8 Section 3 #13

Test 8 Section 3 #13

# 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. )

# Test 5 Section 4 Number 23

Test 5 Section 4 Number 23

# Test 3 Section 4 #26

Test 3 Section 4 #26

# Test 1 Calculator OK #16

Test 1 Calculator OK #16

# Test 2 Section 4 #25

Could you please explain Test 2 Calculator Active #25

# Test 7 Section 4 Number 28

Test 7 Section 4 Number 28

# Test 7 Section 3 #19

Test 7 Section 3 #19