Question

a point moves so that it's y-coordinate is always 2 less than it's x-coordinate.
1) write an equation for it's path
2)where does it cross the x-axis
3) where does it cross the y-axis
4) what is it's slope

Answer 1

Step-by-step explanation:

y is always 2 less than x

1) y = x- 2

2) where does it cross the x-axis ? that means y = 0.

0 = x - 2

x = 2

3) where does it cross the y-axis ? that means x = 0

y = 0 - 2 = -2

4) the slope is always the factor of x.

in

y = x - 2.

the factor of x is simply +1.

Answer 2

If its y-coordinate is always 2 less than its x-coordinate, this is expressed as y = x - 2

Slope and equations

From the given information

• Let the y-coordinate be y
• Let the x-coordinate be x

If its y-coordinate is always 2 less than its x-coordinate, this is expressed as:

y = x - 2

The equation of the path is y - x - 2

2) The point where th line cuts the x-axis is at y = 0

0 = x - 2

x = 2

The point is at (2, 0)

3) The point where th line cuts the y-axis is at x = 0

y = 0 - 2

y = -2

The point is at (0, -2)

4) The standard equation of a line is y = mx + b where m is the slope. Given the equation y = x - 2

Comparing:

mx = 1x

m = 1

Hence the slope of the equation is 1

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