Question #cfb72

1 Answer
Jun 24, 2015

y=2/7x+1

Explanation:

To write an equation for a line, we are going to use the slope and y-intercept.

Looking at the equation of the existing line: y = 2/7 x -3, we see that it is in slope-intercept form ( y=mx+b ) where m, the slope, is 2/7.

We're looking for a line that is parallel to this line; for this second line to be parallel, it must have the same slope.

If we know both the slope and a point that the line goes through, we can find the y-intercept.

Starting with:
y=mx+b

Substitute our slope, color(orange)[2/7]:
y=color(orange)[2/7]x+b

And our point, (color(green)7,color(blue)3):
color(blue)3=2/7*color(green)7+b

Now we can simplify - first cancel out the 7s:
3 = 2 + b

Subtract both sides by 2:
3 - 2 = b
1 = b

Now we have all the information we need to write an equation for our new line. To write the equation for this line, we can use the familiar slope-intercept form.

Starting with our formula:
y=mx+b

Substitute our slope, color(orange)[2/7] and y-intercept b, color(purple)1:
y=color(orange)[2/7]x+color(purple)1

...and we're done!

It's always good to double check our work - one way to do that is to graph both equations. We can also plug our (x,y) of (color(green)7,color(blue)3) into our equation to make sure it actually passes through that point (since we're confident that our slope is correct). If we do that and simplify, we'll see that:
color(blue)3=2/7*color(green)7+1
3 = 2+1
3 = 3