Geometry. I already know the answer. Need to know how to solve. The equation of a line is y = –2x + 1. What is the equation of the line that is parallel to the first line and passes through (2, 2)?

Question

lefinnois · Answer

The answer's y = –2x + 6. How do I solve?

lefinnois · Answer

Thanks for checking out my question @.Sam. Would you like to help out or are you just here for browsing?

.sam. · Answer

If the lines are parallel the gradient will be the same

.sam. · Answer

-2 will be your gradient

.sam. · Answer

Are you able to follow?

lefinnois · Answer

Unfortunately not.

lefinnois · Answer

I'm unfamiliar with the terminology "gradient"

.sam. · Answer

Gradient means slope

.sam. · Answer

They have the same meaning

lefinnois · Answer

this is going to sound embarrassing but I'm uncertain as to a slope. I've definitely heard the word, though. That's where the line goes, yes?

lefinnois · Answer

I don't know how I would identify the gradient in an equation, though.

.sam. · Answer

A slope is like a slanted line on the graph, if the slope is zero, the line will be straight

.sam. · Answer

By straight I mean horizontal or vertical

adrimit · Answer

the slope of a line is equivalent to asking how much higher would i be if i traveled along the line in the positive horizontal direction

adrimit · Answer

horizontal only @.Sam.

.sam. · Answer

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lefinnois · Answer

Okay, so to find the slope in the equation, it's always the only with a variable, yes?

adrimit · Answer

do you know any calculus?

.sam. · Answer

He/She barely knows what slope is how could he/she know any calculus?

lefinnois · Answer

Lol. Unfortunately, I'm not very knowledgeable with regards to mathematics. I sadly do not know any calculus.

lefinnois · Answer

Anyways, the slope stays the same and I identify the slope but it because the one with the variable, right?

adrimit · Answer

ok do you know how to find the y-intercept of a line?

lefinnois · Answer

Nope. :-)

adrimit · Answer

the y-intercept is where the line "intercepts" or meets the y axis

lefinnois · Answer

And that would be +1?

adrimit · Answer

yep

lefinnois · Answer

Okay, so how would I make it parallel?

lefinnois · Answer

And pass through 2, 2. I have no clue, honestly.

adrimit · Answer

now do you know where you can find the slope of your line y=-2x+1?

lefinnois · Answer

It's -2

adrimit · Answer

good. now take an equation of the form y=mx+b, where m is the slope and b is to be determined

.sam. · Answer

You have y=-2x+1, comparing to the equation of a straight line y=mx+c, the 'm' will be your slope, and that is -2. Then, use the equation again y=mx+c, and from the coordinates we have 'y' being 2, and 'x' being 2, and 'm' being -2 to construct your new equation. It's just that simple.

lefinnois · Answer

Good good. :-) So y=mx+c is the parallel formula?

lefinnois · Answer

@.Sam. ?

adrimit · Answer

now to find b, just plug in the slope and the coordinates of any point on the line (i.e. (-2,-2)) y=mx+b is the "slope-intercept" form of a line ingeneral