Question

1) Write the equation parallel to the following equations that would go through (2,7):

Answer 1

Note: Your option 'b' is somewhat ambiguous, so I am assuming you meant to write the equation y=2x+3 for the 'b' option.

Answer:

the equation y = 2x + 3  has slope m=2 and the y-intercept is 3, and also PASSES through the point (2, 7).

Step-by-step explanation:

• An equation parallel to the given line equation will have the same slope.

Given the point (2, 7) from which the equation passes through.

so checking all the equations in the options to check whether any equation passes through or not.

Checking the option 'a':

y = 3x - 2

Putting (2, 7)

7=3(2)-2

7=6-2

7=4

L.H.S is not equal to R.H.S

Therefore, the option 'a' is NOT correct.

So, the equation y = 3x - 2 will NOT PASS through the point (2, 7)

Checking the option 'b':

y = 2x + 3

Putting (2, 7)

7=2(2)+2

7=7

7=7

L.H.S is equal to R.H.S

Therefore, option 'b' is the CORRECT option.

So, the equation y = 2x + 3 will PASS through the point (2, 7)

Checking the option 'c':

y = x-6

Putting (2, 7)

7=2-6

7=-4

L.H.S is not equal to R.H.S

Therefore, the option 'c' is NOT correct.

So, the equation y = x-6 will NOT PASS through the point (2, 7)

Checking the option 'd':

y + 2x = 8

Putting (2, 7)

7+2(2)=8

7+4=8

11=8

L.H.S is not equal to R.H.S

Therefore, the option 'd' is NOT correct.

So, the equation y + 2x = 8 will NOT PASS through the point (2, 7)

Therefore, considering the above analysis, we conclude that:

Option 'b' is the CORRECT option.

So, the equation y = 2x + 3 will PASS through the point (2, 7).

also

The slope-intercept form of the equation is

$y=mx+b$

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

Therefore, the equation y = 2x + 3  has slope m=2 and the y-intercept is 3, and also PASSES through the point (2, 7).