Question

Using the above​ technique, find the equation of the line containing the points (-2,7) (4,-2)

Answer 1

Explanation:

Hey there!.

The equation of a st.line passing through points (-2,7) and (4,2) is;

`(y - y1) = (y2 - y1)/(x2 - x1) (x - x1)`

Put all values.

`(y - 7) = (2 - 7)/(4 + 2) (x + 2)`

Simplify it to get answer.

`(y - 7) = ( - 5)/(6) (x + 2)`

`6(y - 7) = - 5(x + 2)`

`6y - 42 = - 5x - 10`

`5x + 6y - 42 + 10 = 0`

`5x + 6y - 32 = 0`

Therefore the required equation is 5x+6y-32=0.

Hope it helps...

Answer 2

Equation of a line = y = mx +b

m = slope = change in y over the change in x

b = y intercept:

m = (-2 - 7) / (4 - -2) = -9/6 = -3/2

Now you have y = -3/2x + b

Use one of the points, replace y and x and solve for b:

7 = -3/2(-2) + b

Simplify:

7 = 3 + b

Subtract 3 from both sides:

b= 4

The equation is y = -3/2x + 4