Question

Question #d8011

Answer 1

`y=3x+4" is correct"`

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(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 coordinate points"`

The 2 points here are (0 ,4) and (1 ,7)

let `(x_1,y_1)=(0,4)" and " (x_2,y_2)=(1,7)`

`rArrm=(7-4)/(1-0)=3/1=3`

Either of the 2 points may be used as `(x_1,y_1)` as both lie on the line.

`"Using "m=3" and " (x_1,y_1)=(1,7)`

Substitute these values into the equation.

`y-7=3(x-1)larrcolor(red)" in point-slope form"`

distributing and simplifying gives an alternative version of the equation.

`y-7=3x-3rArry=3x-3+7`

`rArry=3x+4larrcolor(red)" in slope-intercept form"`