SAT Math: Practice Questions-Heart of algebra-Graphing linear equations

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Question

What is the graph of the equation y=3^{x} ?

Answer/Explanation

Ans: A

Question

A patio is to be made using square paving stones that are all the same size. There will be no gaps between the paving stones, and they will not overlap. The line in the \(xy\)-plane above represents the relationship between the area \(y\), in square feet, of the patio and the number of paving stones, \(x\), used to make the patio. The top surface of each paving stone is a square with side length \(k\) feet. What is the value of \(k\)? 

  1. 1
  2. 2
  3. 3
  4. 4
Answer/Explanation

Ans: B

Question

Line \(l\) is shown in the \(xy\) plane above. Which of the following is an equation of line \(l\) ?

  1. \(5x-2y=10\)
  2. \(5x+2y=10\)
  3. \(2x-5y=10\)
  4. \(2x+5y=10\)
Answer/Explanation

Ans : D

Question

The graph of \(y=\frac{3}{5}x-8\) in the \(xy\)- plane is a line. What is the slope of this line?

Answer/Explanation

Ans: .6, 3/5

Question

\(y=(\frac{-1}{2})x-7\) 
\(y=-5x-7\)

Which of the following graphs in the \(xy\)-plane represents the equations in the given system?

Answer/Explanation

Ans: D

Question

Line \(p\) is shown in the \(xy\)-plane. Line \(q\) (not shown) is perpendicular to line \(p\) and also passes through. Which of the following point lies on line \(q\) ? 

  1. (-1,0)
  2. (0,-1)
  3. (0,1)
  4. (1,1)
Answer/Explanation

Ans: B

Question

The graph of the equation 4\(x\)+3\(y\)=\(q\), where \(q\) is a constant, is a line in the \(xy\)- plane. What are the coordinates of the point at which the line crosses the \(x\)-axis? 

  1. (\(\frac{q}{3}\),0)
  2. (\(\frac{q}{4}\),0)
  3. (\(\frac{3}{q}\),0)
  4. (\(\frac{4}{q}\),0)
Answer/Explanation

Ans: B

Question

The function \(h\) is defined by \(h\)(\(x\)) = -\(\frac{1}{4}x-2\) . Which is the graph  of \(y\) = \(h\)(\(x\)) ? 

Answer/Explanation

Ans: D

Question

A line in the \(xy\)-plane has a slope of 1 and passes through the point (0, 2). Which is an equation of the line?

  1. \(y\)=\(x\)/2
  2. \(y\)=2\(x\)
  3. \(y\)=\(x\)+2
  4. \(y\)=\(x\)-2
Answer/Explanation

Ans: C

Question

For the linear function \(f\), \(f\)(2) = 10 and the graph of \(y\) = \(f\)(\(x\)) in the \(xy\)-plane has a slope of 3. Which equation defines \(f\)?

  1. \(f\)(\(x\)) = 2\(x\) + 12
  2. \(f\)(\(x\))=2\(x\)+8
  3. \(f\)(\(x\)) = 3\(x\) + 10
  4. \(f\)(\(x\))=3\(x\)+4
Answer/Explanation

Ans: D

Question

Line \(l\), is shown in the \(xy\)-plane, and the point with coordinates (2, \(c\)) is on line \(l\). What is the value of \(c\)?

Answer/Explanation

Ans: 12/5, 2.4

Question

The line shown models the possible combinations of the number of goats and horses a certain 10-acre farm can sustain, based on the number of acres of land each animal needs. Based on this model, how many acres of land on the farm does each horse need?

  1. 2
  2. 5
  3. 6
  4. 12
Answer/Explanation

Ans: A

Question

.

Line \(m\) is shown in the \(xy\)-plane. Line \(p\) (not shown) is perpendicular to line \(m\). Which of the following could be the equation of line \(p\)?

  1. \(\frac{1}{2}x+7\)
  2. 2\(x\)+7
  3. \(\frac{-1}{2}x+7\)
  4. -2\(x\)+7
Answer/Explanation

Ans: A

Question

3\(x\)+4\(y\)=16

The given equation models the number of 3-credit-hour courses, \(x\), and the number of 4-credit- hour courses, \(y\), that Camila can take for a total of 16 credit hours next semester. Which graph models this relationship?

Answer/Explanation

Ans: A

Question

What is the \(x\)-intercept of the graph of 8\(x\) + 6\(y\) = 24 in the \(xy\)-plane?

  1. (3, 0)
  2. (4, 0)
  3. (6,0)
  4. (8, 0)
Answer/Explanation

Ans: A

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