Question

How do you write an equation of a line given point (0,1) and (5,3)?

Answer 1

`y=2/5x+1`

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 the slope use the "color(blue)"gradient formula"`

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

`"let "(x_1,y_1)=(0,1)" and "(x_2,y_2)=(5,3)`

`rArrm=(3-1)/(5-0)=2/5`

`"using "m=2/5" and "b=1to(0,color(red)(1))`

`rArry=2/5x+1larrcolor(red)"equation of line"`

Answer 2

`y = 2/5 x + 1` or

`5x - 2y = 5`

Explanation:

The general line through `(a,b)` and `(c,d)` is

`(c-a)(y - b)=(d-b)(x-a)`

Can you see why? When `(x,y)=(a,b)` both sides are zero, and when `(x,y)=(c,d)` both sides are `(c-a)(d-b).`

Substituting,

`(5-0)(y-1) = (3-1)(x-0)`

`5 y - 5 = 2x`

`5y = 2x + 5`

`y = 2/5 x + 1`

Check:

`2/5(0) + 1 = 1 quad sqrt`

`2/5 (5) + 1 = 3 quad sqrt`