Parralel Equation?? Help

Question

Write an equation in slope intercept form for the line that passes through the given point and is parallel to the following equation

Point: (3,1)

Equation: 2x+y=5

Answer 1

y = mx + b is called the slope-intercept form of a line. You will see this form a lot. In this formula, m is the slope (equal to the (change in y) / (change in x)), while b is where the line crosses the y-axis (the "y-intercept")

2x + y = 5 can be re-arranged to y = -2x + 5

By inspection, we can see -2 is the slope.

Parallel lines have equal slope. So we know the equation for the parallel line will have m=-2.

Another form for the equation of a line is the point-slope form: y-y₀ = m (x - x₀)

where m=slope and (x₀,y₀) is a point that the line passes through.

y - 1 = -2 (x - 3)

y = -2x + 7

Check: -2(3) + 7 = -6 + 7 = 1 so y=1 when x=3. Yes, the line passes through (3,1)

Answer 2

In order to have one line parallel to another, they should have the same slope and different y-intercepts. For your original line, y=-2x-5, you have a slope of -2. So we know that the line passing through the point (3,1) should also have slope -2, so they're parallel. Once we have the parallel part down, we can "fix" the line by manipulating its vertical shift "b" so that it passes through what we want.

So we look at y=-2x + b (b is the vertical shift we get to play with, and -2 is from the fact that we need a slope of 2 for the lines to be parallel), and we plug in the point (3,1).

So we have 1 = -2(3) + b, and in order for this to be a true statement, b must be 7.

Our final line, parallel to the original and passing through (3,1) is y = -2x + 7.