Step by step
The question
Question: is y = 2x − 3 proportional?
y = 2x − 3
Proportional means: y divided by x is always the same number.
We call that number k.
Then y = k times x.
proportional: y ÷ x is always the same
k = y ÷ x, y = kx
1 Look at the equation
Put x = 0 in.
y is −3, not 0.
A proportional y is 0 when x is 0: k times 0 is 0.
= x = 0: y = 2 × 0 − 3 = −3
Careful!
It is a straight line.
But it does not go through 0.
The minus 3 spoils it.
Careful: a straight line, but not through (0, 0)
So it is not proportional.
= not proportional
2 Check
Let's check on a graph.
We put the points on the grid.
The line crosses the y-axis at −3, not at 0.
It misses (0, 0).
So the answer is right!
Let's look back.
First: look at the equation.
Last: check.
Answer
= not proportional