Question

1.The table represents a linear function. Find the values of a, b, and c. Show your work.

2.Write the equation for the line graphed below.

3.Layla and Sam are both dog sitters. Layla charges $2 per day plus a sign-up fee of $3. Sam charges a flat rate of $3 per day. The system of linear equations below represents y, the total amount earned in dollars for x days of dog sitting.

a)Write the equation to represent Layla’s fees.
b)Write the equation to represent Sam’s fees.
c)After how many days do Layla and Sam earn the same amount for dog sitting?
What is that amount?

PLEASE HELP

Answer 1

1. a= 1

b=10

c=9

2.y=1/2x-1

3. a) y=3x + 0

b) y=2x+3

c)3

d) $9

Explanation:

1. The values in the x-axis increase by 2 hence a=3-2=1 and c=7+2=9. For the y-values, they increase by 1.

2. The equation of the line can be written in the slope form of y=mx+c where m is the gradient of the line and c is the y-intercept

Taking points on the line ; (-2,-2) and (2,0) the gradient m is ;

m=Δy/Δx Δy=0--2=2 Δx=2--2=4 m=2/4⇒1/2

From the graph c= -1

The equation y=1/2x-1

3

(a) Equation representing Layla fees is;

Taking points (1,3) and (2,6) the gradients is

m=Δy/Δx (6-3)/(2-1) = 3/1 =3

Taking m=3, point (1,3) and (x,y) the equation will be;

m=Δy/Δx

3=y-3/x-1

3(x-1) = y-3

3x-3 = y-3

3x-3+3=y

y=3x + 0 ------equation for Layla line

(b) Equation representing Sam line for fees is

Taking points (1,5) and (2,7) where c=3

m=Δy/Δx

m=7-5/2-1

m=2/1 =2

Equation : y=2x+3

c) The point of intersection of the lines which is 3 days

d)The amount is $9