Question

What is the equation of the line that passes through (3, -7) and (-2, 4)?

Answer 1

`y=-11/5x-2/5`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`

`"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,-7)" and "(x_2,y_2)=(-2,4)`

`rArrm=(4-(-7))/(-2-3)=11/(-5)=-11/5`

`rArry=-11/5x+blarr" partial equation"`

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

`"using "(-2,4)`

`4=22/5+brArrb=-2/5`

`rArry=-11/5x-2/5larrcolor(red)" in slope-intercept form"`