FIND SLOPE X AND Y INTERCEPT FOR THE GIVEN LINE WORKSHEET

Find

(a) gradient

(b) x-intercept and

for the equation of line.

(1) 2x–3y = 6

(2) 4x+5y = 20

(3) y = -2x + 5

(4) x = 8

(5) y = 5

(6) x + y = 11

7) In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope-intercept form that models this situation.

8) In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.

9) In order to become a member of the library-all-star-members club, there is a $40 sign-up fee and a $2 monthly fee. Write an equation in slope-intercept form that models this situation. Find the total cost of being an all-star library member for 19 months.

10) The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2015. Which of the following linear models predicts the population, y, of Florida (in millions) in terms of x, the number of years since 2010.

A. y = 17.4x + 0.22 B. y = -0.22x + 17.4

C. y = 0.22x + 17.4 D. y = -17.4x + 0.22

11) Suppose that a bike rents for $4 plus $1.50 per hour. Write an equation in slope-intercept form that models this situation.

12) In order to join a yoga club there is a $100 annual fee and a $5 fee for each class you attend. Write an equation in slope-intercept form that models this situation.

1. Solution :

2x-3y = 6

m = -coefficient of x/coefficient of y

m = -2/(-3)

m = 2/3

x-intercept :

Put y = 0

2x-3y = 6

2x-0 = 6

x = 3

y-intercept :

Put x = 0

0-3y = 6

-3y = 6

y = -2

So, the required slope, x and y intercepts are 2/3, 3 and -2 respectively.

2. Solution :

4x+5y = 20

m = -coefficient of x/coefficient of y

m = -4/5

x-intercept :

Put y = 0

4x+0 = 20

4x = 20

x = 5

y-intercept :

Put x = 0

0+5y = 20

5y = 20

y = 4

3. Solution :

The given equation is in slope intercept form.

We compare y = - 2x + 5 and y = mx + b we get,

m = - 2 and b = 5

Then we find the x-intercept form,

Let y = 0

By applying y = 0 in given equation, we get

y = - 2x + 5

0 = - 2x + 5

2x = 5

x = 5/2

4. Solution :

Standard form of linear equation.

ax+by+c = 0

x-8 = 0

x+0y-8 = 0

m = -coefficient of x/coefficient of y

m = 1/0

Slope(m) = undefined

x-intercept = 8

y-intercept = 0

5. Solution :

Standard form of linear equation.

ax+by+c = 0

y-5 = 0

0x+y-5 = 0

m = -coefficient of x/coefficient of y

m = 0/1

m = 0

x-intercept = 0

y-intercept = 5

6. Solution :

x+y = 11

m = -coefficient of x/coefficient of y

m = -1/1

m = -1

x-intercept :

Put y = 0

x+0 = 11

x = 11

y-intercept :

Put x = 0

0+y = 11

y = 11

7. Solution :

Start up = y-intercept = $30

Monthly fee = Slope (m) = 4

Equation of the line :

y = m x + b

y = 4x + 30

So, the equation models the information is y = 4x + 30.

8. Solution :

Start up = y-intercept = $20

Monthly fee = Slope (m) = 5

Equation of the line :

y = m x + b

y = 5x + 20

So, the equation models the information is y = 4x + 30.

9. Solution :

Monthly fee = slope = $2

y = m x + b

y = 2x + 40

Here x be the number of months and y is the cost spent.

When x = 19

y = 2(19) + 40

= 38 + 40

= 78

For 19 months, they have to pay $78.

10. Solution :

Initial population at 2010 = 17.4

y-intercept = 17.4

Increases about 0.22 per year, then slope = 0.22

y = mx + b

y = 17.4x + 0.22

So, option A is correct.

Amount spent for rent = $4

y-intercept = 4

Charge per hour = slope = $1.50

Let x the number of hours he is renting and y is amount spent in all.

y = mx + b

y = 1.5x + 4

12. Solution :

Amount spent for annual fee = $100

Amount spent for each class = $5

Let x be the number of classes he is attending and y is the amount spent.

y = 5x + 100

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FIND SLOPE X AND Y INTERCEPT FOR THE GIVEN LINE WORKSHEET

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