The responses to the questions involving the solution and equations of a straight line are;
6. The slope is -0.5
7. The equation is; y = x + 4
8. y = 7 - 0.25•x
9. The balance after m months is modeled by the equation;
B = 1,800 - 150•m
10. The slope is the monthly payment on the loan
How can a straight line equation be analyzed?
6. The points on the graph in question 6 are; (0, 4), and (4, 2)
The slope is given by the ratio of the rise to the run of the graph as follows;
[tex]Slope = \frac{2 - 4}{0 - 4} = - 0.5[/tex]
- The slope of the graph is -0.5
7. The equation in slope and intercept form is found as follows;
The given points are;
(-1, 3), and (-3, 1)
The slope and intercept form is presented as follows;
y = m•x + c
The point and slope form is presented as follows;
y - y1 = m•(x - x1)
Where m is the slope of the graph
m = (1 - 3)/(-3 - (-1)) = -2/-2 = 1
Which gives;
y - 3 = 1 × (x - (-1)) = x + 1
y = x + 1 + 3 = x + 4
The equation of the graph in slope and intercept form is; y = x + 4
8. The points are; (-4, 8), (4, 6)
Which gives;
m = (6 - 8)/(4 - (-4)) = -2/8 = -0.25
Therefore;
y - 8 = -0.25•(x - (-4)) = -0.25•x - 1
y = -0.25•x - 1 + 8 = -0.25•x + 7
9. The amount Zachary purchased the computer on loan = $1,800
The balance after 3 months = $1,350
The balance after 5 months = $1,050
Therefore;
The points on the graph of the equation that models the balance are therefore;
(0, 1,800), (3, 1,350), (5, 1,050)
Which gives;
B - 1800 = ((1,350-1,800)/(3-0))•(m - 0)
B - 1800 = -150•m
The equation that models the balance, B, after m months is therefore;
10. The slope, ((1,350-1,800)/(3-0)) = -150, signifies the amount by which the balance reduces each month, which is the same as the amount Zachary pays each month, (the monthly payment).
Learn more about the equation of a straight line here:
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