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Consider two points P1(2,7) and P2(6,15)...

Consider two points `P_1(2,7)` and `P_2(6,15)`. Write the equation and draw a straight line through these points.

A

`y=2x+3`

B

`y=2x+5`

C

`y=x+3`

D

`2y=2x+3`

Text Solution

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The correct Answer is:
A
Step 1. Obtain the gradient or slope, which is `m`.
Step 2. c can be found by using the `(x,y)` values at any given point.
Step 1. Gradient `=(x_2-y_1)/(x_2-x_1)=(15-7)/(6-2)=("Height")/("Distance")=8/4=2`
So, `y=2x+c`.

Step 2. To find `c`, put `x=2, y=7` or `x=6, y=15` in Eq. (i).
`7=2xx2+cimpliesc=3`
So, `m=2, c=3`.
Hence, the equation becomes `y=2x+3`.
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