![]() ![]() How much does Jenna make in one hour if she sells 5 items during that hour?.She still makes $10 per hour, plus $3 for each item she sells. Yes, she still works there, even after all her thievery, but she'll tell you it has nothing to do with her old man owning the joint. The fourth step, "take a nap," is totally optional. Figure out what question is being asked, and answer that question.Find the linear equation being described.Now that we've practiced turning words into linear equations, let's actually solve a couple of word problems. He may be speedy, but he's not quite speedy enough to turn back time. It doesn't make sense to think about Lukas driving for a negative number of hours, so we leave that part out. Since the y-intercept is 0, the equation of the line isĪgain, notice that we only graphed half of the line. We wonder if all this algebra-talk is distracting Lukas from how homesick he's feeling right about now.Īs for the equation, we can see that the slope of the line is After 3 hours of driving, Lukas was 200 miles from his house, so the point (3, 200) is also on the graph. Since Lukas left from his house, he was 0 miles from his house after 0 hours of driving, so the point (0, 0) is on the graph. Let's have x be the number of hours Lukas has been driving, and Lukas's distance from home depends on how long he's been driving. Anyway, Lukas was 200 miles from home at 3 p.m. In fact, it was so constant we're not entirely convinced he didn't just set a brick on the accelerator, then recline his seat and take a nap. Lukas left his house at noon to go for a drive. Whenever we're writing an equation for a word problem, we need to specify what the variables are. If we want to be fussy, we can also write down the condition The y-intercept is 10, and the slope is 3, so the equation we want is We aren't accounting for the dozens of scarves that Jenna has been sneaking into her bag for herself, in which case she is practically selling a negative number of them, but in the interest of simplicity, let's look the other way and pretend we saw nothing.įrom the graph, we can now write an equation for this line in slope-intercept form. Since it doesn't make sense to have Jenna sell a negative number of items, we only draw the part of the line where x is at least 0. If Jenna sells 1 item she's paid $13, and if she sells 2 items she's paid $16, so the points (1, 13) and (2, 16) are also on the graph: Since Jenna is paid $10 if she sells 0 items, the point (0, 10) will be on the graph. By the way, $3 is quite a commission rate, considering that most of the shop's inventory consists of cheap polyester scarves that sell for $10 a pop. On the graph, the horizontal axis will represent the number of items Jenna sells during one hour, and the vertical axis will represent the amount she gets paid during that hour. The amount Jenna makes depends on how many items she sells, so our independent variable x should be the number of items she sells, and the dependent variable y should be the amount she's paid. She makes $10 per hour, plus $3 for each item she sells. Write and graph the linear equation described by the following statement: The hardest part of word problems is usually translating from English into math, so we'll practice that part first. However, before we bother with those, let's look at some word problems that describe single lines, and we're not referring to orderly rows of petrified eighth graders on their way into a school dance. Lots of word problems can be solved with systems of linear equations. ![]()
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