ANSWERS
13. $195 (24 months) and $130 (11 months)
14. $80 (1 month) and $100 (5 months)
15. 10 months ($125) and 23 months ($190)
16. 5
18. 75
19. y = 5x + 75
EXPLANATION
To answer all of these questions we have to find the equation first.
The equation that relates the account balance (y) to the number of months saving (x) is,
[tex]y=mx+b[/tex]Where m is the slope - also called rate of change, and b is the y-intercept.
The slope of a line passing through points (x1, y1) and (x2, y2) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]We can find the slope by choosing any two pairs of (# of months, account balance). Let's find it with the pairs (2, 85) and (6, 105),
[tex]m=\frac{105-85}{6-2}=\frac{20}{4}=5[/tex]The slope of the line is 5, so for now, the equation is,
[tex]y=5x+b[/tex]To find the y-intercept we have to replace y and x with any pair of points from the table and solve for b. Let's use the first one,
[tex]\begin{gathered} 85=5\cdot2+b \\ b=85-10 \\ b=75 \end{gathered}[/tex]The y-intercept is 75. And the equation is y = 5x + 75.
To find the answers to the questions in parts 13 and 14, we just have to replace x by the number of months given and solve:
• 24 months,
[tex]y=5\cdot24+75=120+75=195[/tex]• 11 months,
[tex]y=5\cdot11+75=55+75=130[/tex]• 1 month,
[tex]y=5\cdot1+75=80[/tex]• 5 months,
[tex]y=5\cdot5+75=25+75=100[/tex]To solve the two questions in part 15 first we have to solve the equation for x. Subtract 75 from both sides,
[tex]\begin{gathered} y-75=5x+75\cdot75 \\ 5x=y-75 \end{gathered}[/tex]And divide both sides by 5,
[tex]\begin{gathered} \frac{5x}{5}=\frac{y-75}{5} \\ x=\frac{1}{5}y-15 \end{gathered}[/tex]So if we want to find the number of months until she saved $125, we have to replace y with 125,
[tex]x=\frac{1}{5}\cdot125-15=25-15=10[/tex]And the same applies to $190,
[tex]x=\frac{1}{5}\cdot190-15=38-15=23[/tex]