Exam 2: Linear Equations in Two Variables and Functions

For over 20 years, the population of Tressel, Ohio has been increasing linearly according to the function $P ( t ) = 325 t + 10,000$ where P is the number of residents, and t is years after 1980. Compute P(0) and interpret its meaning in the context of this problem.

Given that $( - 2 , y )$ and $( 4,6 )$ are points on a line whose slope is $- \frac { 4 } { 3 }$ , find $y$ .

Sketch a graph by completing the table and plotting points. h(x)= -2 -1 0 1 2

A tool rental store charges a flat fee of $9.50 to rent a chain saw, and $3.75 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.

Points are collinear if they lie on the same line. Use the slope formula to determine if thepoints are collinear. (8, -13), (-4, -1), (7, -12)

Use the slope formula to determine the slope of the line containing the two points. $\left( \frac { 8 } { 5 } , - \frac { 9 } { 2 } \right)$ and $\left( - \frac { 3 } { 4 } , \frac { 1 } { 3 } \right)$

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form. The line contains the point $( - 6,19 )$ and is parallel to a line with a slope of $- \frac { 5 } { 2 }$ .

Write an equation of the line satisfying the given conditions. The line is perpendicular to the x-axis and passes through (-4, 8).

For over 20 years, the population of Tressel, Ohio has been increasing linearly according to the function $P ( t ) = 325 t + 7500$ where P is the number of residents, and t is years after 1980. In what year will the population reach 16,925?

Match the equation with the correct graph below. $y = 3$

Plot the point on the rectangular coordinate system. $( 3.3 , - 3.8 )$

At the Jumping Jack cookie factory, quality assurance inspectors remove broken or otherwise defective cookies from a moving conveyor belt prior to packaging. Based on past studies, the plant manager knows that the inspectors eliminate 98% of the defective cookies at a conveyor belt speed of 9 feet per minute. As the belt speed increases, the factory can produce more cookies per hour, but at the cost of lower quality of the packaged product. Inspectors collect only 60% of defective cookies at a belt speed of 18 feet per minute. a. Make a graph with the belt speed on the x-axis and the corresponding inspection efficiency, in percent, on the y-axis. Graph the points (9, 98) and (18, 60). b. Find an equation of the line through the given points. Write the equation in slope-intercept form. Round the slope and y-intercept each to 1 decimal place. c. Use the equation from part (b) to predict the efficiency of the inspectors at a belt speed of 15 feet per minute. Round to the nearest percent.

Two points are given from each of two lines $L _ { 1 }$ and $L _ { 2 }$ . Without graphing the points, determine if the lines are perpendicular, parallel, or neither. $L _ { 1 } : ( 4,3 )$ and $( - 6,13 )$ $L _ { 2 } : ( 2,0 )$ and $( 3 , - 2 )$

Which of the following is a linear function?

Find the domain. Write the answer in interval notation. $z ( a ) = \sqrt { a + 5 }$

For what value(s) of x is f (x) = 3?

Use the slope formula to determine the slope of the line containing the two points. (9, 5) and (9, 8)

Plot the point on the rectangular coordinate system. $\left( - \frac { 7 } { 4 } , - \frac { 5 } { 2 } \right)$

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. 6x+8y=3 x+y=7