Question

The equation of a line is 5x + 10y = 15. Which if the following points lines on the line? (–3, 0) (–1, 2) (1, –2) (0, 3)

Answer 1

divide both sides of the equation by 5 and you get:

x+2y=3 so using the points in order...

-3+0=3  false

-1+4=3 true

1-4=3 false

0+6=3 false

So the only point that lies upon the line given is (-1,2)

Answer 2

We need to find whether certain points lie on a line.

The point (-1,2) satisfies the equation, it lies on the given line.

If we substitute each point in the equation of the line and the equation is true then the point lies on the line or else it does not.

Let us substitute each point on the line.

The equation of the line is $5x+10y=15$

(-3,0)

$5\times -3+10\times 0=-15\neq 15$

This equation is false.

(-1,2)

$5\times -1+10\times 2=-5+20=15$

This equation is true.

(1,-2)

$5\times 1+10\times -2=5-20=-15\neq 15$

This equation is false.

(0,3)

$5\times 0+10\times 3=30\neq 15$

The equation is false.

As it can be seen only the point (-1,2) satisfies the equation, it lies on the given line.

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