Write a function that is parallel to y=2x+4, but passes through (3,14)

Question

y=2x+4

1. y=3x+14
2. y=2x+8
3. y=2x+14
4. y=2x+20

Answer 1

When you compare 2 or more lines, they can either be Perpendicular lines (they intersect each other to create 4 right angles at their intersection - their slopes are Opposite Reciprocals of each other) or they can be Parallel lines (they never intersect. They stay the same distance apart and move at the same rate over time - they have equal slopes), or they can be somewhere in between perpendicular and parallel, where they merely have different slopes of any kind.

The question above is asking you to write a function or equation for a line that is parallel to the line

y = 2x + 4. This function is written in Slope Intercept form (y = mx + b) so the slope (m) is 2.To write an equation for a line parallel to that, then the slope of the new line must also be 2. The other thing is that the new line must pass through the point (3,14). Using our slope of 2 or 2/1, we can figure it out this way:

Starting at (3,14) we will move down 2 and to the left 1, landing at point (3-1, 14-2) or (2,12)

Let's do this again: (2,12) move down 2 and to the left 1, landing at point (2-1, 12-2) or (1,10)

Again: (1,10), move down 2 and left 1, landing at point (1-1,10-2) or (0,8)

(0, 8) will be the Y-INTERCEPT for our new line, so now we have a slope of 2 and a y-intercept of 8 and we can write the equation /function: y = mx + b (m is the slope and b is the intercept)

y = 2x + 8

Answer 2

slope has to be 2, that eliminates a)

plug the point in, it works for b). b) is correct y=2x + 8

14 = 2(3) + 8