Question

Which equations represents the line that pases through points (1,-5) and (3, -17)?

Answer 1

y= -6x +1

Explanation:

The equation of a line is usually written in the form of y=mx +c, where m is the gradient (or slope) and c is the y-intercept.

In order to find the equation of a line, you would need 2 things:

① Gradient (← can be found)

② Coordinate (✓ we have 2 coordinates here)

To find the gradient, use the gradient formula below:

`gradient = (y1 - y2)/(x1 - x2)`

`m = ( - 5 - ( - 17))/(1 - 3) \\ m = ( - 5 + 17)/( - 2) \\ m = (12)/( - 2) \\ m = - 6`

Substitute the value of m into the equation:

y= -6x +c

To find the value of c, substitute a pair of coordinates.

When x=1, y= -5,

-5= -6(1) +c

c -6= -5

c= 6 -5

c= 1

Thus, the equation of the line is y= -6x +1.