Question

What's the equation of a line that passes through (-4,1) and (0,5).?

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)=(-4,1)" and "(x_2,y_2)=(0,5)`

`rArrm=(5-1)/(0-(-4))=4/4=1`

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

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

`"using "(0,5)" then"`

`5=0+brArrb=5`

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

Answer 2

`y+x-5=0`

Explanation:

The formula to get the equation of a straight line knowing two points that lie on it is:
`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

where the two points are `(x_1,y_1)` and`(x_2,y_2)` and you can pick any of the points to be one of them.

And by substituting you get:

`(y-5)/(x-0)=(5-1)/(-4-0)`

And by simplifying you get:
`y-5=-x`
so the equation is `y+x-5=0`