Question

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

Answer 1

`y=3x-11`

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(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(3,-2)" and "(x_2,y_2)=(5,4)`

`rArrm=(4-(-2))/(5-3)=6/2=3`

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

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

`"using "(5,4)`

`4=(3xx5)+brArrb=4-15=-11`

`rArry=3x-11larrcolor(red)"in slope-intercept form"`