Question

Can some one please help me?
Write an equation of the line that is parallel to the given line y = x + 3 and the given point (5,0).

Answer 1

Whats the slope of the given line?

Answer 2

(5,0) is x-intercept @MrDoe

Answer 3

Sigh, first notice that for a parallel line the slope is the SAME. This means the slop of the line we want is just 1. That means we need something of the form:
\[y-y_0=m(x-x_0)\]
Where m = 1. And we have (x_0,y_0)=(5,0)
\[y-0=(1)(x-5) \implies y=x-5\] The way to visualize it is to look at this drawing:

There are infinitely many lines parallel to y=x+3, we only need to use the point to find the one that fits our conditions.

Answer 4

indeed caleb, thanks for catching that, the line passing through (5,0) with a slope of one will be y=x-5

Answer 5

so the slope would be .....1?

Answer 6

sorry i didnt reply faster

Answer 7

When you define a line in slope intercept form you have:
\[y=mx+b\]
Where m is the slope and b is the y-intercept (hence "slope-intercept"). So if there is a 1 or no coefficient (implied 1) in front of the x then the slope is 1.