Answer:
1. [tex]y=-\frac{1}{4}x + 3\frac{1}{4}[/tex]
2. (See picture)
3a. [tex]y=-\frac{300}{4}x + 700[/tex]
3b. Jerry returning $300 back to his father per 4 months
3c. the amount of money Jerry owes to his father
4. [tex]y+8=\frac{1}{4} (x-4)[/tex]
5. [tex]y=-3x+6[/tex]
Step-by-step explanation:
This is going to take a while to explain...
1. Firstly, identify the slope. We can see that the line lands on (1, 3) and (5, 2) (not sure because the graph is off), using the definition of slope, we get:
[tex]m=\frac{3-2}{1-5} \\m=\frac{1}{-4} \\m=-\frac{1}{4}[/tex]
Next, we can replace everything into a point-slope formula:
[tex]y-3=-\frac{1}{4} (x-1)\\y-3=-\frac{1}{4}x + \frac{1}{4} \\y=-\frac{1}{4}x +3\frac{1}{4}[/tex]
That's question 1 done.
2. Start by locating the y-intercept, in this case, is 6. Draw a dot on (0, 6), and then draw the next point using the slope -5/2, go down 5 grids and go 2 grids to the right. Use a ruler to connect both points and draw a straight line across them. It should look something like this:
(See picture)
3a. Using the same method in the first question, we can write down the equation:
[tex]y=-\frac{300}{4}x + 700[/tex]
3b. Since slope means "change in y over change in x", then the change in y means the amount of money that Jerry gives back to his father, and change in x means the time that passes per month. Thus, we can express the slope as "Jerry returning $300 back to his father per 4 months".
3c. The y-intercept is 700, and looking at the parameter at the left, it says "amount owed", thus, it means "the amount of money Jerry owes to his father".
4. We have a point and the slope, enough information to write down a point-slope form equation:
[tex]y-(-8)=\frac{1}{4} (x-4)\\y+8=\frac{1}{4} (x-4)[/tex]
5. We have two points, so we can find the slope of the line, and (0, 6) tells us that the y-intercept is 6:
[tex]m=\frac{-3-6}{3-0} \\m=\frac{-9}{3} \\m=-3[/tex]
With the following information, we can fill in the variables into the point-slope form equation:
[tex]y-6=-3(x-0)\\y-6=-3x\\y=-3x+6[/tex]
Whoosh! I hope everything in number 3 is correct.
