Question

What is the equation of the line passing through `(3,7)` and `(13,19)`?

Answer 1

`y=6/5x+17/5`

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)=(3,7)" and "(x_2,y_2)=(13,19)`

`rArrm=(19-7)/(13-3)=12/10=6/5`

`rArry=6/5x+blarrcolor(blue)"is the partial equation"`

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

`"using "(3,7)" then"`

`7=18/5+brArrb=35/5-18/5=17/5`

`rArry=6/5x+17/5larrcolor(red)"is the equation of line"`