Question

Find an equation for the line below

Answer 1

x-2y=-1

Explanation:

The given given line passes through;

`(-5,-2)` and
`(5,3)`

The slope of the line is given by;

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

We plug in the values to get;

`m=(3--2)/(5--5)=(1)/(2)`

The equation is given by

`y-y_1=m(x-x_1)`

`y--2=(1)/(2)(x--5)`

`2(y+2)=x+5`

2y+4=x+5

The eqation is x-2y=-1

Answer 2

`y=(1)/(2)x+(1)/(2)`

Explanation:

The 2 points in red are (5, 3) & (-5, -2). These are (x_1,y_1) & (x_2,y_2), respectively.

The equation of a line given two points are given by the formula
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

We simply plug in x_1, y_1, x_2, y_2 into the formula and find the equation of the line:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\y-3=(-2-3)/(-5-5)(x-5)\\y-3=(-5)/(-10)(x-5)\\y-3=(1)/(2)(x-5)\\y-3=(1)/(2)x-(5)/(2)\\y=(1)/(2)x-(5)/(2)+3\\y=(1)/(2)x+(1)/(2)\\`