Question

Consider the line y = x + 5. Find the equation of the line that is parallel to this line and passes through the point (-9, -5).

Answer 1

Answer: y = x + 4

Explanation:

We need to find the equation of the line, given that:

⇒ it's parallel to y = x + 5

⇒ it passes through (-9,-5)

To determine a line's equation, we should know two things:

⇒ the slope

⇒ the point

We know the point. To find the slope, we'll focus on the other piece of information: the new line is parallel to y = x + 5.

Recall that two parallel lines have the same slope. Therefore, the new line also has a slope of 1.

Now we can substitute the data into our point-slope equation, which is:

• 
  `\bold{y-y_1=m(x-x_1)}`

`\bold{y-(-5)=1(x-(-9)}`

Simplify:

`\bf{y+5=1(x+9)}`

`\bold{y+5=x+9}`

`\bold{y=x+9-5}`

`\boxed{\bold{y=x+4}}`

Therefore, the equation of the line is y = x + 4.

Answer 2

y = x + 4

Explanation:

the equation of a line in slope- intercept form is

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

given the line with equation

y = x + 5 ← in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes , then

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

to find c , substitute the point (- 9, - 5 ) for x and y into the partial equation

- 5 = - 9 + c ( add 9 to both sides )

4 = c

y = x + 4 ← equation of parallel line