Question

Complete the equation of the line through (-8,8)(−8,8)left parenthesis, minus, 8, comma, 8, right parenthesis and (1,-10)(1,−10)left parenthesis, 1, comma, minus, 10, right parenthesis.

Answer 1

`y = -2x - 8\\OR\\2x+y+8=0`

Explanation:

Given that there are 2 points

`A(-8,8)` and

`B(1,-10)`

So, the coordinates are:

`x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8`

Equation of a line is given as:

`y =mx+c`

where 'm' is the slope of the line, formula for 'm' is given as:

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

`(x,y)` are the points that satisfy the equation of the line.

`c` is the
`y -` intercept.

Calculating the value of m using the given coordinates:

`m=(-10-8)/(1-(-8))\\\Rightarrow m=(-18)/(9) = -2`

So, the equation of line becomes:

`y =-2x+c`

Now, putting the coordinates of point
`A(-8,8)`

`8 =-2* (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8`

Please refer to the graph of given equation of line.

The equation of line is:

`y =-2x+-8\\OR\\2x+y+8=0`