Answer:
y = 2x-5
Explanation:
Lets look for an equation in the standard form of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
A reference line is given: y=2x+3. It has a slope of 2. Parallel lines have the same slope, so the line we are looking for will also have a slope of 3. We can therefore wrtite what we know sio far. The new line will be:
y = 2x+b
Any vale of b will produce a line that is parallel to the referenc elien. But we need a line that goes through a given point of (3,1). By choosingf the correct value of b, we can force the line therough this point. The easiest way to find b is to use the known point in the equiation we have thuis far, and solve for b:
y = 2x+b
1 = 2*(3)+b for (3,1)
b = -5
The equation of a line parallel to y=2x+3 and going through point (3,1) is:
y = 2x-5
See attached graph.