Question

The ordered pairs below represent a linear relation between x and y.

(-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11)

Which of the following is a correct statement about this relation?

A. The slope of the line represented by this table is -2 and the y-intercept is -4.
B. The slope of the line represented by this table is 2 and the y-intercept is 7.
C. The slope of the line represented by this table is 2 and the y-intercept is -4.
D. The slope of the line represented by this table is -2 and the y-intercept is 7.

Answer 1

Slope = rise/run
(-2,3) (0,7)

7-3 /0- -2 = 4/2= 2
When x = 0 y=7 intercept

Answer is B

Answer 2

Option B - The slope of the line represented by this table is 2 and the y-intercept is 7.

Explanation:

Given : The ordered pair below represent a linear relation below x and y.

(-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11)

The slope form is
`y=mx+c`

where m is the slope of line and c is the y-intercept.

or to find slope between two points are
`m=(y-y_1)/(x-x_1)`

Since they are ordered pairs so, there slopes were same

Let take points (-3,1), (-2,3)

`m=(y-y_1)/(x-x_1)`

`m=(3-1)/(-2-(-3))=(2)/(1)=2`

Therefore, the slope of the given linear function is 2

Now, we have to find y intercept we put in slope form

`y=mx+c`

`y=2x+c`

Given pairs are ordered therefore, they satisfy the above equation so let point (-2,3)

`3=2(-2)+c`

`c=3+4=7`

So, slope of the line is 2 and y-intercept is 7.

Therefore, Option B is correct.