Question

How do you write an equation of a line going through (2,1) and (-2,-1)?

Answer 1

`y=1/2x`

Explanation:

Recall that the general equation for a line is:

`color(teal)(|bar(ul(color(white)(a/a)y=mx+bcolor(white)(a/a)|)))`

where:
`y=`y-coordinate
`m=`slope
`x=`x-coordinate
`b=`y-intercept

Determining the Equation of the Line
`1`. Start by labelling the coordinates to either be coordinate `1` or `2`.

Coordinate `1`: `(color(red)(x_1),color(teal)(y_1))=(color(red)2,color(teal)1)`

Coordinate `2`: `(color(blue)(x_2),color(darkorange)(y_2))=(color(blue)(-2),color(darkorange)(-1))`

`2`. Find the slope between the two coordinates using the formula, `m=(y_2-y_1)/(x_2-x_1)`.

`m=(color(darkorange)(y_2)-color(teal)(y_1))/(color(blue)(x_2)-color(red)(x_1))`

`m=(color(darkorange)(-1)-color(teal)1)/(color(blue)(-2)-color(red)2)`

`m=(-2)/(-4)`

`color(violet)(m=1/2)`

`3`. Find the value of the y-intercept by substituting the slope and either coordinate `1` or `2` into `y=mx+b`. In this case, we will use coordinate `1`.

`y=mx+b`

`color(teal)1=color(violet)(1/2)(color(red)2)+b`

`1=1+b`

`b=0`

`4`. Rewrite the equation.

`color(green)(|bar(ul(color(white)(a/a)y=1/2xcolor(white)(a/a)|)))`