Question

How do you write the equation in slope intercept form given (3/4,5/2) and ( - 7/8, 3/2)?

Answer 1

`y=8/13x+53/26`

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)=(3/4,5/2)" and "(x_2,y_2)=(-7/8,3/2)`

`m=(3/2-5/2)/(-7/8-3/4)=(-1)/(-13/8)=8/13`

`y=8/13x+blarrcolor(blue)"is the partial equation"`

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

`"using "(3/4,5/2)" then"`

`5/2=6/13+brArrb=5/2-6/13=53/26`

`y=8/13x+53/26larrcolor(red)"in slope-intercept form"`