What is the slope of the line perpendicular to the one shown below? MAINIMG

Year	2023	Total
Questions	17	17

Year

2023

Total

Questions

Solution & Explanation

Related Formula

m⊥ = -(1)/(m)

where $m$ $m$ is the slope of the given line and $m⊥$ $m_{\perp}$ is the slope of the line perpendicular to it.

Core Logic

Identify two points on the line shown in the graph: $(0, -3)$ $(0, -3)$ and $(4, 0)$ $(4, 0)$.

Calculate the slope $m$ $m$ using the rise over run formula:

m = (y₂ - y₁)/(x₂ - x₁) = (0 - (-3))/(4 - 0) = (3)/(4)

The slope of any perpendicular line is the negative reciprocal of $(3)/(4)$ $\frac{3}{4}$.

Step 1: Calculate Perpendicular Slope

m⊥ = -(1)/(3/4) = -(4)/(3)

Hence, choice C is correct.

Pattern Recognition

Line graph $arrow$ $\rightarrow$ count rise/run to find $m$ $m$. Perpendicular slope is always the negative reciprocal flip.

Chapter Mix

SAT Math: Heart of Algebra

More Heart of Algebra Previous-Year Questions

Q sat_math_2023_01_january_morning Linear Function Word Problems

Mark runs a tutoring service where he charges

for each new client and

\text{\

20

per hour. His new client gets 4 hours of tutoring and pays Mark

100}$. Which of the following statements is correct?

A. Mark was overpaid
B. Mark was underpaid
C. You cannot determine if he was overpaid or underpaid based on the information given.
D. Mark was paid the correct amount for his services.

Solution

Related Formula

Total Cost = Fixed Fee + (Hourly Rate \times Hours)

Core Logic

Calculate Mark's required total fee for a new client getting 4 hours of tutoring:

Fee = $7 + ($20 \times 4) = $7 + $80 = $87

Mark was paid $\$100 $.$

Step 1: Compare Payment with Expected Fee

Since$.

Step 1: Compare Payment with Expected Fee

Since $\ $100 >$ $100 > \$87 $, Mark received$ $, Mark received $\ $13$ $13$ more than his standard charge. Therefore, Mark was overpaid.

Pattern Recognition

Word problem with fixed + variable cost $arrow$ $\rightarrow$ set up total equation, evaluate, compare to actual payout.

Chapter Mix

SAT Math: Heart of Algebra

Q sat_math_2023_01_january_morning Graphing Linear Equations

Which of the following lines has an undefined slope?

Graphing Linear Equations diagram for Q3 - SAT 2023 — A coordinate graph displaying four lines labeled Red Line, Green Line, Blue Line, and Orange Line.

A. Red line
B. Green line
C. Blue line
D. Orange line

Solution

Related Formula

m = (Δ y)/(Δ x)

Core Logic

A vertical line has a constant $x$ $x$-value, which means $Δ x = 0$ $\Delta x = 0$.

Since division by zero is mathematically undefined, vertical lines have an undefined slope.

Looking at the graph, the Blue Line is a vertical line at $x = 2$ $x = 2$.

Step 1: Conclusion

Therefore, the Blue line has an undefined slope.

Pattern Recognition

Horizontal line $arrow$ $\rightarrow$ slope = 0. Vertical line $arrow$ $\rightarrow$ slope is undefined.

Chapter Mix

SAT Math: Heart of Algebra

Q sat_math_2023_01_january_morning Linear Function Word Problems

Megan and her friends all go to buy candy at the store. Mark pays \

15 for 3 chocolate bars, Megan pays

20 for 4 chocolate bars, and Cindy pays \

100 for 20 chocolate bars. Which equation below represents the price per chocolate bar related to the total price of each order? Please note that

represents total price and

x$ represents number of chocolate bars.

A. $5y = x$ $5y = x$
B. $y = 5x$ $y = 5x$
C. $y = x + 5$ $y = x + 5$
D. $15y = 3x$ $15y = 3x$

Solution

Related Formula

$y = kx$ $y = kx$

where $k$ $k$ represents the unit price per item, $x$ $x$ represents quantity, and $y$ $y$ represents total cost.

Core Logic

Determine the unit cost per chocolate bar from each order:

Unit Price = ($15)/(3) = ($20)/(4) = ($100)/(20) = $5

So $k = 5$ $k = 5$.

Step 1: Formulate Equation

Substitute $k = 5$ $k = 5$ into $y = kx$ $y = kx$:

$y = 5x$ $y = 5x$

Thus, option B is correct.

Pattern Recognition

Proportional direct variation $arrow$ $\rightarrow$ total = unit rate $\times$ $\times$ quantity.

Chapter Mix

SAT Math: Heart of Algebra

Q sat_math_2023_01_january_morning Solving Systems of Linear Equations

What is the solution to the system of linear equations demonstrated in the graph?

Solving Systems of Linear Equations diagram for Q6 - SAT 2023 — A graph showing two intersecting lines meeting at (2, 0) on the x-axis.

A. $(0, 2)$ $(0, 2)$
B. $(0, 0)$ $(0, 0)$
C. $(2, 0)$ $(2, 0)$
D. $(2, 2)$ $(2, 2)$

Solution

Related Formula

The solution to a system of linear equations represented graphically is given by the point of intersection $(x, y)$ $(x, y)$ of the lines.

Core Logic

Observe the point where the Red Line and Blue Line intersect on the coordinate plane.

They cross directly on the x-axis at $x = 2$ $x = 2$ and $y = 0$ $y = 0$.

Step 1: Conclusion

Thus, the point of intersection is $(2, 0)$ $(2, 0)$, corresponding to option C.

Pattern Recognition

Graph of system $arrow$ $\rightarrow$ solution is simply the intersection point.

Chapter Mix

SAT Math: Heart of Algebra

What is the slope of the line perpendicular to the one shown below? A Cartesian coordinate plane showing a straight line passing through (0, -3) and (4, 0).

Solution & Explanation

Related Formula

Core Logic

Step 1: Calculate Perpendicular Slope

Pattern Recognition

Chapter Mix

More Heart of Algebra Previous-Year Questions

Solution

Related Formula

Core Logic

Step 1: Compare Payment with Expected Fee

Step 1: Compare Payment with Expected Fee

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 1: Conclusion

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 1: Formulate Equation

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 1: Conclusion

Pattern Recognition

Chapter Mix

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What is the slope of the line perpendicular to the one shown below?
A Cartesian coordinate plane showing a straight line passing through (0, -3) and (4, 0).