Question

Find the equation of the line passing through the points (3,1) and (7,-7)​

Answer 1

y = -2x + 7

Explanation:

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

We are given the point (3,1) and (7,-7), calculate the slope:

`\displaystyle m=(-7-1)/(7-3)`

`\displaystyle m=(-8)/(4)=-2`

m = -2

No w we use any of the given points: (3,1) and substitute in the equation of the line:

y - 1 = -2 ( x - 3 )

Multiplying:

y - 1 = -2x + 6

Adding 1:

y = -2x + 7