Answer:
The equation of the line is:
y
=
5
6
x
−
15
6
Explanation:
The equation of the line will be in the form:
y
=
m
x
+
c
where
m
is the slope (gradient) and
c
is the y-intercept.
To find the slope, we use:
m
=
y
2
−
y
1
x
2
−
x
1
It doesn't matter which point we decide is
(
x
1
,
y
1
)
and which we choose as
(
x
2
,
y
2
, since the formula will work either way.
m
=
0
−
(
−
5
)
3
−
(
−
3
)
=
5
6
Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:
y
=
m
x
+
c
0
=
5
6
(
3
)
+
c
=
15
6
+
c
Rearranging:
c
=
0
−
15
6
=
−
15
6
Over all, then, the equation of the line is:
y
=
5
6
x
−
15
6
The equation of the line is:
y
=
5
6
x
−
15
6
Explanation:
The equation of the line will be in the form:
y
=
m
x
+
c
where
m
is the slope (gradient) and
c
is the y-intercept.
To find the slope, we use:
m
=
y
2
−
y
1
x
2
−
x
1
It doesn't matter which point we decide is
(
x
1
,
y
1
)
and which we choose as
(
x
2
,
y
2
, since the formula will work either way.
m
=
0
−
(
−
5
)
3
−
(
−
3
)
=
5
6
Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:
y
=
m
x
+
c
0
=
5
6
(
3
)
+
c
=
15
6
+
c
Rearranging:
c
=
0
−
15
6
=
−
15
6
Over all, then, the equation of the line is:
y
=
5
6
x
−
15
6
Step-by-step explanation:
We want to find the equation of the line that passes through the points (0, 3) and (5, -3). The linear equation is y = (-6/5)*x + 3
A general linear equation is written as:
y = a*x +b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that the line passes through (0, 3) and (5, -3) then the slope is:
[tex]a = \frac{-3 - 3}{5 - 0} = \frac{-6}{5}[/tex]
Then the line is:
y = (-6/5)*x + b
To get the value of b, we use the fact that the line passes through (0, 3), so we have:
3 = (-6/5)*0 + b
3 = b
Then the linear equation is just:
y = (-6/5)*x + 3
If you want to learn more about linear equations, you can read:
https://brainly.com/question/4074386
