Question

Unit 2: Linear Functions Date: Bell: Homework 3: Writing Linear Equations, Applications


Help!! ILL GIVE 30 POINTS

Answer 1

Slope intercept form is y=mx+b

1. Y= -6x + -23
2. Y= 4/3x + 0.665
3. Y= -1/2x + 9
4. Y= -(1)x + 9

Answer 2

The equation of the lines are given by the points on the line from which

the slope and y-intercept are determined.

Responses;

1. y = -6·x - 23

2. $\underline{y= \frac{4}{3} \cdot x + \frac{2}{3}}$

3. $\underline{y = 9 - \dfrac{x}{2}}$

4. y = 9 - x

5. a) $\underline{V = 30 - \dfrac{1}{21} \times D}$

b) 315 miles

6. a) $\underline{D = 2 + \dfrac{3}{4} \cdot n}$

b) Mikayla will not be ready for the marathon in 12 weeks

How can the equation of a straight line be found?

1.  Slope = -6, passes through (-4, 1)

The point and slope form is; y - 1 = -6·(x - (-4))

Which gives;

y = -6·(x - (-4)) + 1 = -6·x - 24 + 1 = -6·x - 23

• The slope and intercept form y = -6·x - 23

2. Slope = $\frac{4}{3}$; passes through (-5, -6)

The point and slope form is therefore;

y + 6 = $\mathbf{\frac{4}{3}}$·(x + 5)

y = $\frac{4}{3}$·(x + 5) - 6 = $\frac{4}{3} \cdot x + \frac{20}{3} - 6 = \mathbf{\frac{4}{3} \cdot x + \frac{2}{3}}$

Which gives;

• $\underline{y= \frac{4}{3} \cdot x + \frac{2}{3}}$

3. Points on the line are; (-4, 11) and (2, 8)

$Slope = \dfrac{8 - 11}{2 - (-4)} = \dfrac{-3}{6} = -\dfrac{1}{2}$

The equation is therefore;

$y - 8 = -\dfrac{1}{2} \cdot (x - 2) = 1 - \dfrac{x}{2}$

$y = 1 - \dfrac{x}{2} + 8 = \mathbf{9 - \dfrac{x}{2}}$

• $\underline{y = 9 - \dfrac{x}{2}}$

4. The points are; (6, 3), (14, -5)

$Slope = \dfrac{-5 - 3}{14 - 6} =-1$

Equation: y - 3 = -1·(x - 6)

y = 6 - x + 3 = 9 - x

• y = 9 - x

5) Volume of gas tank = 30 gallon

Distance Troy's truck gets per gallon = 21 miles

a) The equation representing the amount of gas in in Troy's truck, V, is

presented as a linear equation as follows;

The slope of the equation is the number of gallons per mile = $-\frac{1 \, gallon}{21 \, mile}$

The slope is negative given that the gas in the tank is reducing.

The y-intercept is the amount of gas initially in the tank = 30 gallons

• $The \ equation \ is \ \underline{V = 30 - \dfrac{1}{21} \times D}$

b) Given that the tank is half full, we have;

Volume of gas in the tank = $\dfrac{30 \, gallons}{2}$ = 15 gallons

Which gives;

$15 = \mathbf{ 30 - \dfrac{1}{21} \times D}$

Therefore;

D = 315

• The number of miles Troy has driven, D = 315 miles

6. a) The initial distance Mikayla is able to run = 2 miles

The distance by which the distance is increased each week = Three-quarters of a mile.

The equation is therefore;

• $\underline{D = 2 + \dfrac{3}{4} \cdot n}$

Where;

D = The distance Mikayla runs

n = Number of weeks

b) The distance of the half marathon = 13.1 miles

Time at which the marathon takes place = In 12 weeks time

The distance Mikayla will be able to run in 12 weeks is given by

plugging in 12 in the given equation as follows;

$D = 2 + \dfrac{3}{4} \times 12 = \mathbf{ 11}$

• The distance Mikayla is able to run in 12 weeks = 11 miles, therefore, Mikayla will not be ready to run 13.1 miles in 12 weeks

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