Question

How do you write the equation of the line parallel to y=3x-1 that passes through the point (-3, -5)?

Answer 1

parallel means identical slopes, so m=3, and using pt-slope form, Y-Y1=m(x-x1), the parallel line is Y+5=3(X+3)
so Y=3X+9-5
So........................Y=3X+4

Y=3X+4 is the eqtn.

Answer 2

Wow. Dude can um you explain that to me?

Answer 3

So, two lines are only parallel if they have the same slopes.

You can write a simple line in the form y = mx + b, where m is the slope and b is the y-intercept -- the y value the graph of the function runs through when x = 0.

Answer 4

You are given one function, which is \(y = 3x - 1\). This tells you that the slope for the second line must be 3 in order for it to be parallel.

The only thing you have left to find out then is the y-intercept that will let the line go through the point (-3, -5).

A point is a pair, (x, y) that gives you an X value and Y value that are on the line. Since you have m, you can say:

$$ y = 3x + b $$
$$ (-5) = 3 \cdot (-3) + b $$

Here we plugged in the point that we want to be on the line -- (-3, -5) -- into our equation. Then, we can solve for b:

$$ -5 - (3 \cdot (-3)) = b $$

This will give us the value of b, which we can then plug back into the equation:

$$ y = 3x + (-5 - (3 \cdot (-3))) $$