Question

Find the equation of the line with a gradient of -1/2 that passes through (4,9) Use algebraic methods ?

Answer 1

`y=-1/2x+11`

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 gradient and `(x_1,y_1)" a point on the line"`

`"here "m=-1/2" and " (x_1,y_1)=(4,9)`

Substitute these values into the equation.

`rArry-9=-1/2(x-4)larrcolor(red)" in point-slope form"`

distributing the bracket and simplifying gives an alternative version of the equation.

`y-9=-1/2x+2`

`rArry=-1/2x+2+9`

`rArry=-1/2x+11larrcolor(red)" in slope-intercept form"`