1. Answer true or false to each statement and explain your answers.
a. The straight-line graph of a linear equation slopes upward unless the slope is 0.
b. The value of the y-intecept has no effect on the direction that the straight-line graph of a linear equation slopes.
2. Richard's Heating and Cooling in Prescott, Arizona, charges $55 per hour plus a $30 service charge. Let x denote the number of hours required for a job and let y denote the total cost to the customer.
a. Obtain the equation that expresses y in terms of x.
b. Find b0 and b1.
c. Construct a table for x-values 0.5, and 2.25 hours
d. Draw the graph on a equation that you obtained in part (a) by plotting the points from part (c) and connecting them with a straight line.
e. Apply the graph from part (d) to estimate visually the cost of a job that takes 1.75 hours. Then calculate that cost excately by using the equation from part (a).
3. A ball is thrown straight up in the air with an initial velocity of 64 feet per second (ft/sec). According to the law of physics, of you let y denote the velocity of the ball after x seconds, y=64-32x.
a. Determine b0 and b1 for this linear equation.
b. Determine the velocity of the ball after 1,2,3, and 4 sec.
c. Graph the linear equation y=64-32x, using the four points obtained in part (b)
d. Use the graph from part (c) to estimate visually the velocity of the ball after 1.5 sec. Then calculate that velocity excatly by using the linear equation y=64-32x.
4. For the following three equations,
i). y=30 + 55x (from question 1)
ii). y= -1 + 2x
iii). y= -8 - 4x
a. find the y-intercept and slope
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation
The solution is a detailed guide on the straight line equation. It explains how to find the slope and y-intercept of the line. It also shows how to graph the line.