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

D

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, - 5) and (x₂, y₂ ) = (- 3, - 7)

m =
`(-7+5)/(-3+1)` =
`(-2)/(-2)` = 1, hence

y = x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation

Using (- 3, - 7), then

- 7 = - 3 + c ⇒ c = - 7 + 3 = - 4

y = x - 4 → D

Answer 2

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

Let's first find the slope. Below is how you find the slope using two points:

The formula for slope is

`(y_(2)-y_(1))/(x_(2)-x_(1))`

In this case we have the two points:

(-1, -5) and (-3, -7)

This means that:

`y_(2) =-7\\y_(1) =-5\\x_(2) =-3\\x_(1) =-1`

^^^Plug these numbers into the formula for slope...

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

`(-2)/(-2)`

1

^^^This is your slope

This is the formula we have so far:

y = 1x + b

OR

y = x + b

Now we must find b

To do that you must plug in one of the given points the line goes through in the x and y of the equation.

(-1, -5)

-5 = 1(-1) + b

-5 = -1 + b

-4 = b

(D) y = x - 4

Hope this helped!

~Just a girl in love with Shawn Mendes