Question

A line passes through (2,-8) and (-6,-3) . Find the equation

Answer 1

y = -5/8x - 27/4

Step-by-step explanation:

1.) Figure out the slope. We do this by dividing the difference of y-coordinates by the difference of x-coordinates. By doing this, you will get -3-(-8) divided by -6-2, which is equal to -5/8.

2.) Now, by using the point (2, -8) and the slope, you can substitute these points into the slope-point formula to get your equation. If you do this, you would get y + 8 = -5/8 (x - 2), which is simplified to y = -5/8x -27/4.

Answer 2

1
x
+
−
4
y
=
−
6

Step-by-step explanation:
First, we need to determine the slope of the line passing through the two points. The slope can be found by using the formula:
m
=
y
2
−
y
1
x
2
−
x
1
Where
m
is the slope and (
x
1
,
y
1
) and (
x
2
,
y
2
) are the two points on the line.
Substituting the values from the points in the problem gives:
m
=
3
−
2
6
−
2
=
1
4
Next, we can use the point-slope formula to find an equation for the line. The point-slope formula states:
(
y
−
y
1
)
=
m
(
x
−
x
1
)
Where
m
is the slope and
(
x
1
y
1
)
is a point the line passes through. Substituting the slope we calculated and the first point from the problem gives:
(
y
−
2
)
=
1
4
(
x
−
2
)
The standard form of a linear equation is:
A
x
+
B
y
=
C
Where, if at all possible,
A
,
B
, and
C
are integers, and A is non-negative, and, A, B, and C have no common factors other than 1. We can convert the equation in point-slope form to standard form as follows:
First, we need to remove the fraction as all coefficients must be integers. We will multiply each side of the equation by
4
:
4
(
y
−
2
)
=
4
×
1
4
(
x
−
2
)
(
4
×
y
)
−
(
4
×
2
)
=
4
×
1
4
(
x
−
2
)
4
y
−
8
=
1
x
−
2
Next, we will add
8
and subtract
1
x
from each side of the equation to isolate the
x
and
y
terms on the left side of the equation:
−
1
x
+
4
y
−
8
+
8
=
−
1
x
+
1
x
−
2
+
8
−
1
x
+
4
y
−
0
=
0
+
6
−
1
x
+
4
y
=
6
Now, we will multiply each side of the equation by
−
1
to make the
x
coefficient a positive integer:
−
1
(
−
1
x
+
4
y
)
=
−
1
×
6
1
x
+
−
4
y
=
−
6