Yr9 Coordinate Geometry

[confused-]

7) The line which passes through 2 points (2,y) and (5.9) has a gradient of 2.
a. Find the value of y

I did this:
2=(9-y)/(5-2)
1/5=y/2
2/10=5y/10
2=5y
y=2/5

but answer at the back of the book is 3.


New Question:
14) The line parallel to y=4x - 5 is:
A. y=2x-5
B. 4x + y + 2 = 0
C. 2y=4x-10
D. 4x-y-1=0

Is there any way to figure this out other than trial and error on a number plane? Or do I just rearrange things in y=4x - 5?
The answer is D.

 

[mmm4444bot]

I did this:

2=(9-y)/(5-2) This is good.

1/5=y/2 This is strange.

BTW, if I were to solve 1/5=y/2 for y, then I would multiply both sides by 2. We only need to get a common denominator when adding or subtracting ratios (fractions).

2/10=5y/10
2=5y
y=2/5

What we have is a proportion; that is, two equal ratios. The approach is different.

We can simplify the numerator, to start.

2 = (9 - y)/3

Now, multiply both sides by 3, to clear both the algebraic fraction and the parentheses on the righthand side.

Then finish.

New Question:
14) The line parallel to y=4x - 5 is:
A. y=2x-5
B. 4x + y + 2 = 0
C. 2y=4x-10
D. 4x-y-1=0

Is there any way to figure this out other than trial and error on a number plane? Or do I just rearrange things in y=4x - 5?

Yes, solve each of the equations for y; then you'll be able to see the slope (gradient) of each line.

You're looking for the choice whose slope is the same as the slope in the given line y = 4x - 5.