Question

How do you write an equation in slope intercept form given that the line passes through the points (-1,1) and (2,3)?

Answer 1

`y=2/3x+5/3`

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"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-1,1)" and "(x_2,y_2)=(2,3)`

`rArrm=(3-1)/(2-(-1))=2/3`

`rArry=2/3x+blarrcolor(blue)"is the partial equation"`

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

`"using "(2,3)" then"`

`3=4/3+brArrb=9/3-4/3=5/3`

`rArry=2/3x+5/3larrcolor(red)"in slope-intercept form"`