Question

How do you find an equation of the line containing the given pair of points. (2,4) and (6,6)?

Answer 1

`y=1/2x+3`

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"`

`m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(2,4)" and "(x_2,y_2)=(6,6)`

`rArrm=(6-4)/(6-2)=2/4=1/2`

`rArry=1/2x+blarrcolor(blue)"is the partial equation"`

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

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

`4=1+brArrb=4-1=3`

`y=1/2x+3larrcolor(red)"in slope-intercept form"`