Question

What is the equation of the line passing through `(13,7)` and `(37,47)`?

Answer 1

`5x-3y=44`

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)=(13,7)" and "(x_2,y_2)=(37,47)`

`rArrm=(47-7)/(37-13)=40/24=5/3`

`rArry=5/3x+blarrcolor(blue)"is the partial equation"`

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

`"using "(13,7)" then"`

`7=65/3+brArrb=21/3-65/3=-44/3`

`rArry=5/3x-44/3larrcolor(red)"in slope-intercept form"`

`"multiply all terms by 3 and rearrange"`

`rArr3y=5x-44`

`rArr5x-3y=44larrcolor(red)"in standard form"`