Grade 12 Math: Linear Relationships
This worksheet focuses on advanced linear relationships, including graphing, equations, and real-world applications for Grade 12 students.
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Grade 12 Math: Linear Relationships
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. Graph the linear equation \(y = -2x + 3\) on the coordinate plane below. Clearly label at least two points on the line.
2. The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) represents the and \(b\) represents the .
3. A horizontal line has a slope of , while a vertical line has an slope.
4. Which of the following equations represents a linear function?
\(y = x^2 - 4\)
\(y = 3x - 5\)
\(y = \sqrt{x} + 2\)
\(y = |x| + 1\)
5. Write the equation of a line that passes through the points \((2, 5)\) and \((4, 11)\) in slope-intercept form.
6. A taxi service charges a flat fee of $3.00 plus $2.50 per mile. Write a linear equation that models the total cost \(C\) for a ride of \(m\) miles.
7. The graph of \(y = -4x + 7\) has a positive slope.
True
False
8. Parallel lines have the same slope but different y-intercepts.
True
False
9. A company's profit (P) in thousands of dollars can be modeled by the equation \(P = 0.5t - 1.2\), where \(t\) is the number of years since 2010. What was the company's profit in 2015? In what year will the company's profit reach $8,800?
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