How do you find the equation of the line that goes through (1,- 3) and ( 0,8)?

2 Answers
Oct 1, 2017

y=-11x+8

Explanation:

First, we find the slope using (y^2-y^1)/(x^2-x^1)

Therefore, m=(8-(-3))/(0-1) which is equal to m=-11

To get the line, the equation would be y=mx+b

y=11x+b

We will put in (1, -3) as x=1 and y=-3
-3=(-11)1+b->
-3=(-11)*1+b->
-3=-11*1+b->
-3=-11+b->
8=b (Add 11 to both sides of the equation)

8=b

Therefore, the line will be y=mx+b->

y=-11x+8 graph{y=-11x+8 [-10, 10, -5, 5]}

Oct 1, 2017

11x+1y=8

Explanation:

For a straight line the slope between any two points is the same for all pairs of points on the line.

By slope we mean the ratio of the difference between the y coordinates divided by the difference between the x coordinates.

color(white)("xxxx")"slope"=(delta y)/(delta x)=(y_2-y_1)/(x_2-x_1)
color(white)("xxxxxx")for two points (x_1,y_1) and (x_2,y_2)

For a general point (x,y) and the point (1,-3) (this is one of the given points,
we have
color(white)("xxxx")"slope"=(y-(-3))/(x-1)=(y+3)/(x-1)
and
for the two given points (0,8) and (1,-3)
we have
color(white)("xxxx")"slope" = (8-(-3))/(0-1)=11/(-1)=-11

Since the slope must be the same for all pairs of points on a straight line
color(white)("XXX")(y+3)/(x-1)=-11

While is is a valid equation that answers the given question, it would be normal to convert this into standard Ax+By=C form:

color(white)("XXX")(y+3)=-11(x-1)

color(white)("XXX")y+3=-11x+11

color(white)("XXX")11x+y+3=11

color(white)("XXX")11x+1y=8

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

When doing this kind of problem it is always a good idea to verify that the derived equation satisfies the given points:

For (x,y)=(1,-3)
color(white)("XXX")11 * (1)+1 * (-3)=11-3=8 ... as required
and
for (x,y)=(0,8)
color(white)("XXX")11 * (0) + 1 * (8)= 0+8=8 ...again, as required.