Question

Question 4 Multiple Choice Worth 4 points)

(05.02)
Two quantities are related, as shown in the table:
х у
2 10
4 9
6 8
8 7
Which equation best represents the relationship?
y = 1/2x + 11
y = -1/2x + 11
y = 2x + 10
y = 2x + 11

Answer 1

Question No 4

The equation will be:
`y=-(1)/(2)x+11`

Option B is correct answer.

Question No 5

The equation will be:
`y=(3)/(4)x+4`

Option A is correct answer.

Explanation:

Question 4

The option equations are in slope intercept forms, so we will write equation in slope intercept form.

The general equation of slope intercept form is:
`y=mx+b` where m is slope and b is y-intercept

Finding Slope:

Using the point (2,10) and (4,9) we can find slope

The formula used is:
`Slope=(y_2-y_1)/(x_2-x_1)`

Putting values and finding slope:

`Slope=(9-10)/(4-2)\\Slope=-(1)/(2)`

So, we get slope m = - 1/2

Finding y-intercept

Using point (2,10) and slope m =1/2 we can find y-intercept

`y=mx+b\\10=-(1)/(2)(2)+b\\10=-1+b\\b=10+1\\b=11`

So, equation will be:

`y=mx+b\\y=-(1)/(2)x+11`

Option B is correct answer.

Question 5

The option equations are in slope intercept forms, so we will write equation in slope intercept form.

The general equation of slope intercept form is:
`y=mx+b` where m is slope and b is y-intercept

Finding Slope:

Using the point (0,4) and (4,7) from the graph we can find slope

The formula used is:
`Slope=(y_2-y_1)/(x_2-x_1)`

Putting values and finding slope:

`Slope=(7-4)/(4-0)\\Slope=(3)/(4)`

So, we get slope m = 3/4

Finding y-intercept

Using point (0.4) and slope m = 3/4 we can find y-intercept

`y=mx+b\\4=(3)/(4)(0)+b\\4=0+b\\b=4`

So, equation will be:

`y=mx+b\\y=(3)/(4)x+4`

Option A is correct answer.