1) (a) State the equation of the vertical line passing through the point (-3, 6).
(b) Where does the vertical line in Part (a) intersect the x-axis? Provide the coordinates (x, y) of the point.
(c) State the equation of the horizontal line passing through the point (3, -4).
(d) Where does the horizontal line in Part (c) intersect the y-axis? Provide the coordinates (x, y) of the point.
(e) Where do lines in Part (a) and the line in Part (c) intersect? Provide the coordinates (x, y) of the point.
HINT: Graph the points and lines to answer the questions.
2) Which of the following is TRUE about the line through the points (-2, 3) and (-2, -3)? Explain, and then circle your answer.
A. The slope is undefined.
B. The slope is positive.
C. The slope is 0.
D. The slope is negative.
3) (a) Solve the inequality 3(2 + 4x) ≤ 1 - (9 - 5x). Show work, and then circle your answer.
A. x ≤ - 2
B. x ≤ -14/17
C. x ≥ -2
D. x ≥ -14/17
(b) Solve the inequality -x > -7 + 4.
4. (a) Which of the following equations does the graph represent? Show work or explanation, and then circle your answer.
A. y= - (4/3) x + 4
B. y= - (3/4) x - 3
C. y= (3/4) x + 3
D. y = (4/3) x+4
(b) What is the y-intercept of the line? Use correct notations (paired data (x, y)) representing the y-intercept.
5) (a) What is the equation of a line having slope -4 and passing through the point (5, -1)? Show work/explanation.
(b) Showing your work, find the intercepting points of the line with the x-axis and the y-axis. Show each point as paired data (x, y).
6. (a) Pat purchased a mattress set which was on sale (20% off). 7.5% sales tax and then a $40 delivery charge were added. A total of $1,394.50 was charged to her credit card. What was the purchase price (the sale price) of the mattress set (before the tax and delivery charge)? Show algebraic work/explanation. Write a sentence to answer the question.
(b) Calculate the original (before-the-sale) price of the mattress set purchased. Show your work.
7) (a) Solve, using substitution or elimination by addition (your choice). Show work.
y - 4x = 7
5y - 7x = 9
(b) Test your answers and state your conclusion. Show your work.
8. Consider the linear equation 2x + 8y = 8.
(a) Write the linear equation in slope-intercept form.
(b) State the value of the slope.
(c) State the x-intercept for this line.
(d) Find the coordinates of a point on this line other than the x-intercept. (There are infinitely many right answers! Just find one of them.)
9) A guitar factory has a cost of production C(x) = 75x + 50,000. Showing your algebraic work,
(a) If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up your answer to the nearest dollar.
(b) Write the revenue function R(x).
10. Life expectancy at birth is the estimated lifespan of a baby born in a particular year (given the conditions of that time period). The U.S. life expectancy of a baby born in 1960 was 69.8 years. For a birth year of 2010, the U.S. life expectancy was 78.5 years. Let y be the U.S. life expectancy for a baby born in the year x, where x = 0 represents the year 1960.
(a) Find a linear equation which could be used to predict the U.S. life expectancy y of a baby born in a given year x, where x = 0 represents the year 1960. The slope of your linear equation should be accurate to three decimal places, i.e., to the nearest thousandth. Explain/show work.
(b) Use the equation from part (a) to estimate the U.S. life expectancy for a baby born in the year 2020. Show some work.
(c) Interpret the slope of the equation in part (a). What is the slope and what does it represent in the context of this application involving U.S. life expectancy?