Answer:
Explanation:
We'll look for an equation in the format y = mx + b where m is the slope and b the y-intercept. A characteristic of parallel lines is that they have the same slope. That means the same value of m for both equations.
The reference equation is y = 1/3x + 5, It has a slope of (1/3). This means the new line will also have a slope of (1/3), and so we can write:
y = (1/3)x + b
Any value of b will result in a parallel line to y = 1/3x + 5. But the new line comes with the requirement that it go through point (3,5). That's easily done if we choose the correct value for b, the y-intercept. We could graph the line to visually determine what value of b will make the line go through this point, or we can simply enter the given point in the above equation and solve for b:
y = (1/3)x + b (for point (3,5)
5 = (1/3)(3) + b
5 = 1 + b
b = 4
A b value of four will shift the line so that it intersects (3,5). See the attached graph.