Question

How do you write a linear function equation that passes through points (-2,5) and (-4,7)?

Answer 1

`y=-x+3`

Explanation:

The equation of a line in `color(blue)"point-slope form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

To calculate m, use the `color(blue)"gradient formula"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`
where `(x_1,y_1),(x_2,y_2)" are 2 points on the line"`

The 2 points here are (-2 ,5) and (-4 ,7)

`rArrm=(7-5)/(-4-(-2))=2/(-2)=-1`

Use either of the 2 given points for `(x_1,y_1)`

substitute m = - 1 and (-2 ,5) into the equation.

`y-5=-1(x+2)rArry-5=-x-2`

which simplifies to.

`y=-x+3`