Question

What is the equation of the line that passes through the points (2, 4) and (3,9)?

Answer 1

5

Explanation:

Use `(y_2-y_2)/(x_2-x_1)`

`(4-9)/(2-3)` = `(-5)/-1`

`=5`

Answer 2

`y=5x-6`

Explanation:

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

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

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

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(2,4)" and "(x_2,y_2)=(3,9)`

`m=(9-4)/(3-2)=5/1=5`

`y=5x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute either of the 2 given points"`
`"into the partial equation"`

`"using "(2,4)" then"`

`4=10+brArrb=4-10=-6`

`y=5x-6larrcolor(red)"is the equation of line"`