Question

Determine the equation of the line passing through the points (0,−4) and (−1,−4).

Answer 1

Step - 1: Finding the slope of the line.

The slope of a line passing through points (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) can be written as

m=

x

2

​

−x

1

​

y

2

​

−y

1

​

​

Slope of the line passing through (-1,-4) and (3,0),

m=

3−(−1)

0−(−4)

​

=1

Step - 2: Finding the equation of the line.

The equation of a general line can be written as,

y−y

1

​

=m(x−x

1

​

)

y−(−4)=1(x−(−1))

y+4=x+1

x−y−3=0

Thus, the equation of the line is x - y - 3 = 0.

Step-by-step explanation:

Answer 2

Given:

There are given two points:

`(0,-4),(-1,-4)`

Step-by-step explanation:

According to the question:

We need to write the equation of a line.

So,

To find the equation of the line, first, we need to find the value of the slope.

So,

From the formula of slope:

`m=(y_2-y_1)/(x_2-x_1)`

Where,

`x_1=0,y_1=-4,x_2=-1,y_2=-4`

Put all the values into the given slope formula:

So,

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(-4+4)/(-1-0) \\ m=0 \end{gathered}`

Now,

From the formula to find the equation of line:

So,

`y-y_1=m(x-x_1)`

Then,

`\begin{gathered} y-y_(1)=m(x-x_(1)) \\ y-(-4)=0(x-0) \\ y+4=0 \\ y=-4 \end{gathered}`

Final answer:

Hence, the equation of lie is shown below:

`y=-4`