Question

Find the equation of the line passing through (1, 5) and parallel to y = 3x – 1.

Answer 1

The answer is:

y = 3x + 2

Work/explanation:

If two lines are parallel to each other, their slopes are equal.

Consider the given equation, y = 3x - 1. Its slope is 3. Hence, the slope of the line that is parallel to y = 3x - 1 is 3.

So far, the equation is y = 3x + b.

Now, there are two ways we could find b. We could use point slope, and simplify to slope intercept, or, we could plug the point directly into the equation y = 3x + b, and solve for b. Allow me to demonstrate both ways.

`\rule{350}{3}}`

`\frak{Method~1-Point~slope~form}`

The equation is
`\sf{y-y_1=m(x-x_1)}`, where m = slope and (x₁,y₁) is a point on the line.

Plug in the data

`\sf{y-5=3(x-1)}`

Simplify

`\sf{y-5=3x-3}`

`\sf{y=5x-3+5}`

`\sf{y=3x+2}`

Hence, the equation is y = 3x + 2. Now I will use the second method, and see if I obtain the same answer!

`\rule{350}{3}`

`\frak{Method~two-Slope~intercept~\mid~~Plugging~the~point~into~the~equation}`

Plug the point (1,5) directly into the equation y = 3x + b; plug in 1 for x, and 5 for y.

`\sf{5=3(1)+b}`

Simplify

`\sf{5=3+b}`

`\sf{5-3=b}`

`\sf{2=b}`

Hence, the y intercept is 2; and the equation is y = 3x + 2.

As you can see, I have used two different ways, and I have arrived at the same answer.

Answer 2

Explanation:

Y = mx + b is a line equation in slope intercdept form slope = m

y = 3x-1 has slope m = 3 <==== Parallel slope is also '3'

then using the pont slope form of a line :

(y-5) = 3 (x-1) is the new line

re-arrange to y = 3x +2