Question

Write the equation of the line that passes through the points (1,4) and (5,8) in standard form.

Answer 1

1) we find the slope of this line:
Given two points, (x₁,y₁) and (x₂,y₂) the slope of the line passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)

In this case, we have the points (1,4) and (5,8) and the slope will be:
m=(8-4)/(5-1)=4/4=1

2)Point-slope form of a line:
We need a point (x₀,y₀) and the slope (m);
y-y₀=m(x-x₀)

we can chooso either point of this line (1,4) or (5,8) the end result will be the same.
For example, we choose the point (1,4);
y-y₀=m(x-x₀)
y-4=1(x-1)    (point-slope form          y-y₀=m(x-x₀))
y=x-1+4
y=x+3             (slope-intercept form      y=mx+b)
-x+y=3            (standard form     Ax+By=C)        

if we choose the point (5,8)
y-8=1(x-5)          (point-slope form)
y=x-5+8
y=x+3
-x+y=3

Therefore:

Answer: D. -x+y=3

Answer 2

First find the slope
for points (x1,y1) and (x2,y2)
the slope is (y2-y1)/(x2-x1)

points are (1,4) and (5,8)

slope is (8-4)/(5-1)=4/4=1

y=mx+b
m=slope
y=1x+b
y=x+b
find b

(1,4) given
(x,y)
x=1 and y=4 is a point
sub to find b

4=1(1)+b
4=1+b
minus 1 both sides
3=b

y=x+3
minus  x both sides
-x+y=3

D is the answer