Question

24)The table represents some points on the graph of a linear function. Which function represents the same relationship?

Answer 1

Answer:

A) D) g(x) = 2x - 8

2) B) y = 3/4x - 1 and y = -4/3x + 9

Step-by-step explanation:

1)

In the table, we have the points

(5, 2)

(7, 6)

(9, 10)

(10, 12)

This seems to be a linear relationship, so let's try that:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1)

If we use the first two points, we get the slope:

a = (6 - 2)/(7 - 5) = 4/2 = 2

if we use the first and last point, we get the slope:

a = (12 - 2)/(10 - 5) = 10/5 = 2

Then we can conclude that this is a linear relationship with a slope equal to 2.

y = 2*x + b

To find the value of b, we can just replace any of the points of the data table in the equation, for example, i will use the point (5, 2).

this means that x = 5, and  y = 2.

2 = 2*5 + b

2 = 10 + b

2 - 10 = b

-8 = b

Then the equation is:

y = 2*x - 8

the correct option is: D) g(x) = 2x - 8

2) Here we have two lines, notice that we can with just looking at the image, know the y-intercept of each line.

The one with a positive slope (grows to the right) has a y-intercept = - 1.

The one with a negative slope (grows to the left) has a y-intercept =  9.

The two options that match this condition are:

B) y = 3/4x - 1 and y = -4/3x + 9

C) y = 3/4x - 1 and y = -3/4x + 9

Where the only difference is the slope of the black line.

so et's check which slope matches that line.

In the graph we can see that it passes through the points:

(0, 9) and the point (6, 1)

Then the slope is:

a = (1 - 9)/(6 - 0) = -8/6 = -4/3

Then the correct option is where the negative slope is -4/3, that one is

B) y = 3/4x - 1 and y = -4/3x + 9