Question

Write the equation of a line parallel to x + 2y = 10 and crosses through the point (4,-3) in Slope intercept . Graph the two lines

Answer 1

What is the slope of the line? Can you find it?

Answer 2

So let’s take \(x+2y=10\) and convert it into \(y=mx+b\) form.

\(x+2y=10\) subtract x from both sides
\(2y=-x+10\) divide both sides by 2 to get y by itself
\(y=-\dfrac{1}{2}x+5\)

Now, if we go graph this, at “x=4”, the point of this line is (4,3)

So assuming that you graph the line here, the line itself shifts down from 3 to -3, which is a 6 value difference

That would make the equation look something like this.
\(y=-\dfrac{1}{2}x+5-6\)
Which if we simplify, would give us this.
\(y=-\dfrac{1}{2}x-1\)

(I recommend you read all of this if you want to understand it.)