Question

What is the slope-intercept form of the line passing through `(-4, 1)` and `(-3, 5)`?

Answer 1

`y=4x+17`

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)=(-4,1)" and "(x_2,y_2)=(-3,5)`

`rArrm=(5-1)/(-3-(-4))=4/1=4`

`rArry=4x+blarrcolor(blue)"is the partial equation"`

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

`"using "(-3,5)" then"`

`5=-12+brArrb=5+12=17`

`rArry=4x+17larrcolor(red)"in slope-intercept form"`