What is an equation of the line that passes through the points (0,3) and (5,-3)? Put your answer in fully reduced form.

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: