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6. Check here for instructional material to complete this problem. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Find the slope of the line. OA. m= (Type an integer or a simplified fraction.) O B. The slope is undefined.5: Instructional Material The slope of the line is its tilt or steepness. Line with positive slope Line with negative slope Line with slope of [l Here are some phrases related to slope that you may have heard. use change in y Slope = = . run change In x trig1'1 x2'li1 The slope of the line m between the points 0:131) and (X232) can be given by m 2 Example: Find the slope ofthe line given in the following graph. Begin by locating two points on the line. We will use the points {1,1} and (2, 2), although you could use any two points on the line. III IIFEIIIII. IIIII You could then either use the formula or map out the rise over run from the graph. 21_ 3_ Formula method F2 F1 m _ _x2x1 21 1 '3 Rise-Over-Run Method Let's look at this problem as if we are travelling from (2, - 2) to (1,1). The rise from - 2 to 1 is 3 units. The run from 2 to 1 is - 1. The run is negative because we went to the left, which is the direction of the neg on the number line. (You could have also traveled from (1, 1) to (2, - 2), which has a rise of - 3 and a run of 1, resulting in the same slope.) rise 3 m= - 3 run -1 Answer: The slope is - 3.7. Check here for instructional material to complete this problem. The y-intercept is What is the y-intercept of the line shown in the graph below? (Type an ordered pair.) 7: Instructional Material The y-intercept(s) of a graph is (are) the point(s) where a graph crosses the y-axis. For a line, there is at most one y-intercept. Any y-intercept should be written as an ordered pair in the format (0,b), where b is the y-coordinate of the y-intercept. Example: Find the y-intercept of the graph Looking at the graph, we can see that the line clearly crosses through the y-axis at the point (0,4). Answer: The y-intercept of the line is (0,4).Print 8. Check here for instructional material to complete this problem. For the spring semester 2009, part-time students at a college paid $445 per credit (unit or hour) for tuition and paid a mandatory part-time student fee of $30 per semester. Let T be the total one-semester cost (in dollars) of tuition plus part-time student fee for c credits of classes. Complete parts a. through d. a. Find the slope of the linear model that describes this situation. What does it mean in this situation? The slope is The tuition increases by $ per credit. b. Find an equation of the model. T= (Type an expression using c as the variable.) c. Perform a unit analysis of the equation found in part b. Choose the correct choice below. O A. The unit of the expression on the left side of the equation is credits, but the unit of the expression on the right side of the equation is dollars, which suggests that the equation is incorrect. O B. The unit of the expression on the left side of the equation is dollars, but the unit of the expression on the right side of the equation is credits, which suggests that the equation is incorrect. O C. The units of the expressions on both sides of the equation are dollars, which suggests that the equation is correct. O D. The units of the expressions on both sides of the equation are credits, which suggests that the equation is correct. d. What was the total one-semester cost of tuition plus part-time student fee for 6 credits of classes? 8: Instructional Material rise change in y The average rate of change is the change in some quantity (the rise) divided by the change in units, usually time (the run). The rate of change can be expressed by slope. The average rate of change = slope = run change in x You can find an equation of a line to model this by using your initial amount as your y-intercept and the rate of change as your slope. That is, y = slope . t + initial amount at time 0. Example: A person's salary was $35,000 in 2015 and $60,000 in 2020. Find the average rate of change of the salary per year. Find an equation to describe the salary at t years since 2005. $25,000 The change in salary (the rise) was $60,000 - $35,000 = $25,000. The change in time (the run) was 2020 - 2015 =5 years. Therefore, the average rate of change (the slope) was = $5,000. 5 The vertical axis intercept will be given by the initial amount at time t= 0 which was $35,000. We will use s for salary. The equation will be s = slope . t + initial amount = $5,000t + $35,000. Answer: The average rate of change was $5,000 per year. The equation for salary in s dollars t years from 2015 is s = 5,000t + 35,000.9. Check here' for instructional material to complete this problem. Find the y-intercept of y = =x - 3. The y-intercept of y = -x - 3 is (Type an ordered pair.) 9: Instructional Material For any linear equation written in slope-intercept form, y = mx + b. The y-intercept can be written as (0,b). That is, the constant value b is the y-coordinate of the y-intercept. Example: Find the y-intercept of the line y = 7x - 3. The equation is written in the form y = mx + b. The value of b is - 3. Since the y-intercept should be written as an ordered pair (0,b), the y-intercept for this line is (0, - 3). Answer: The y-intercept is (0, - 3).10. Check here" for instructional material to complete this problem. Refer to the graph sketched to the right. Find y when x = 6. y = "Type an integer or a decimal. Do not round.) X - 10 8 6 6 8Prin 10: Instructional Material There are an innite number of points on a line You can represent each point on a line as a set of paired data (x,y) All ordered pairs that represent solutions to the linear equation are points that lie on the line Points that are not on the line are not solutions to the linear equation. Example in the tollowmg graph, the horizontal axis represents the height of human beings and the vertical axis represents the weight of human beings Find the weight (in pounds) for somebody who IS 60 inches tall o 20 40 so so me Height The horizontal axis represents height and the vertical axis represents weight So, we begin by locating the given value of height: 60 on the horizontal axis and then move up to locate the point on the given line Then, we look overto the vertical axis and nd the corresponding yevalue. o 20 40 so so 100 Hem The corresponding weight tor a height of 60 inches looks to be about 1375 pounds' since it is halfway between 125 and 150 pounds Answer 1375 pounds