Question

Write the equation of a line that passes through the points (4, 2) and
(2, 6).

Answer 1

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Find the gradient of the line first.

Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.

Gradient = (6-2) ÷ (2-4) = -2

Eqn is y = -2x + c

Substitute either one of the coordinates of the points into the equation to find c.

2 = -2(4) + c

c = 10

Equation of the line is y = -2x + 10

Answer 2

WE WILL FIRST FIND THE SLOPE BETWEEN THE POINTS

`m = (y2 - y1)/(x2 - x1) \\ m = (6 - 2)/(2 - 4) \\ m = (4)/( - 2) \\ m = - 2`

I WILL USE POINT (2,6) TO GET THE VALUE OF c

`6 = - 2(2) + c \\ 6 = - 4 + c \\ c = 6 + 4 \\ c = 10`

since the general equation of a straight line is given by y=mx+c

`y = - 2x + 10`

ATTACHED IS THE SOLUTION