Question

Can someone help me with this worksheet please

Answer 1

1. To find for the linear function from this problem, we use the formula:

x/a + y/b = 1

where a is the x intercept and b is the y intercept

x/-9  +  y/3 = 1

Multiply everything by -9:

x – 3y = -9

Rearranging:

3y = x + 9

 

y = (1/3) x + 3

 

2. The general form of a linear function is:

y = mx + b

where m is the slope and b is the y-intercept

y = (-2/5) x + b

when y = 0, x = 1 therefore the b is:

0 = -2/5 + b

b = 2/5

 

y = (-2/5) x + 2/5

 

3. We create two equations from the general form y = mx + b or f(x) = mx + b

-5 = (1/6) m + b

-10 = (1/2) m + b

Subtract the two equations:

-5 - -10 = (1/6 – ½) m

5 = -1/3 m

m = -15

y = -15x + b

using any pair to get the value of b:

-5 = -15 (1/6) + b

b = -2.5

 

y = -15x – 2.5

 

4. same steps with number 3

-2/3 = (1) m + b

2 = (2/3) m + b

Subtract the two equations:

-2/3 - 2 = (1 – 2/3) m

-8/3 = 1/3 m

m = -8

y = -8x + b

using any pair to get the value of b:

2 = -8(2/3) + b

b = 22/3

 

y = -8x + 22/3

 

5. From the graph we have the points:

(-5, 4) and (4, -4)

So we create two equations:

4 = (-5) m + b

-4 = (4) m + b

Subtract the two equations:

4 - -4 = (-5 - 4) m

8 = -9 m

m = -8/9

y = (-8/9) x + b

using any pair to get the value of b:

4 = (-8/9) (-5) + b

b = -4/9

 

y = (-8/9) x – 4/9

 

6. From the graph we have the points:

(2, -5) and (4, 6)

So we create two equations:

-5 = (2) m + b

6 = (4) m + b

Subtract the two equations:

-5 - 6 = (2 - 4) m

-11 = -2 m

m = 5.5

y = 5.5 x + b

using any pair to get the value of b:

-5 = 5.5 (2) + b

b = -16

 

y = 5.5 x – 16

 

7. We can actually solve this easily by plotting the points. We can see that by plotting the points, a curve line is created, not a straight one.

<check the graph photo attached>

 

8. Let us say that the x intercept, a = 1 and the y intercept, b = 1. Prove that slope m = -1

From the equation:

x/a + y/b = 1

x/1 + y/1 = 1

x + y = 1

y = -x + 1

 

Hence slope is m = -1