Question

What is the slope-intercept form of the line passing through `(-1, 4)` and `(-4, 1)`?

Answer 1

`y=x+5`

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)=(-1,4)" and "(x_2,y_2)=(-4,1)`

`m=(1-4)/(-4-(-1))=(-3)/(-3)=1`

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

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

`"using "(-4,1)" then"`

`1=-4+brArrb=1+4=5`

`y=x+5larrcolor(red)"in slope-intercept form"`