Question

Which is an equation of the line that passes through (–1, –5) and (–3, –7)?

a)

y = 2x + 4


b)

y = x – 4


c)

y = –2x + 4


d)

y = –x – 4

Answer 1

Answer: Option b)

`y=x-4`

Explanation:

The equation of a line in the intersecting slope form has the following form:

`y=mx+b`

Where

m is the slope

`m=(y_2-y_1)/(x_2-x_1)` Where
`(x_1, y_1)` and
`(x_2, y_2)` are two points that belong to the line

`b=y_1-mx_1`

In this case the points are: (–1, –5) and (–3, –7)

So:

`m=(-7-(-5))/(-3-(-1))`

`m=(-7+5)/(-3+1)`

`m=(-2)/(-2)`

`m=1`

Therefore

`b=-5-1*(-1)`

`b=-5+1`

`b=-4`

Finally the equation of the line is:

`y=x-4`

Answer 2

For this case we have that by definition, an equation of the line of the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have two points through which the line passes, then we find the slope:

`(x1, y1): (- 1, -5)\\(x2, y2): (- 3, -7)`

`m = \frac {y2-y1} {x2-x1} = \frac {-7 - (- 5)} {- 3 - (- 1)} = \frac {-7 + 5} {- 3 + 1} = \frac {-2} {- 2} = 1`

Then, the equation is of the form:

`y = x + b`

We substitute a point and find b:
`-5 = -1 + b\\-5 + 1 = b\\b = -4`

Finally we have:

y = x-4

Answer:

Option B