Question

i. a set of points where the coordinates of each point have a sum of 2 ii. a set of points where the y-coordinate of each point is 10 less than its x-coordinate to statements about their coordinates:

Explanation:

To solve for the equations of the sets of points:

Part (i)

Step 1: Define the variables

Let the coordinates of a point be \((x, y)\).

Step 2: Translate the condition into an equation

The problem states that the sum of the coordinates is 2. So, we have:
\[
x + y = 2
\]
We can rewrite this in slope - intercept form (\(y=mx + b\)) to better understand the graph. Solving for \(y\):
\[
y=-x + 2
\]
This is the equation of a straight line with a slope of \(- 1\) and a \(y\) - intercept of 2.

Part (ii)

Step 1: Define the variables

Let the coordinates of a point be \((x, y)\).

Step 2: Translate the condition into an equation

The problem states that the \(y\) - coordinate is 10 less than the \(x\) - coordinate. So, we can write the equation as:
\[
y=x - 10
\]
This is the equation of a straight line with a slope of \(1\) and a \(y\) - intercept of \(-10\).

Final Answers

i. The equation of the set of points is \(\boldsymbol{y=-x + 2}\) (or \(\boldsymbol{x + y=2}\))
ii. The equation of the set of points is \(\boldsymbol{y=x - 10}\)

Answer:

To solve for the equations of the sets of points:

Part (i)

Step 1: Define the variables

Let the coordinates of a point be \((x, y)\).

Step 2: Translate the condition into an equation

The problem states that the sum of the coordinates is 2. So, we have:
\[
x + y = 2
\]
We can rewrite this in slope - intercept form (\(y=mx + b\)) to better understand the graph. Solving for \(y\):
\[
y=-x + 2
\]
This is the equation of a straight line with a slope of \(- 1\) and a \(y\) - intercept of 2.

Part (ii)

Step 1: Define the variables

Let the coordinates of a point be \((x, y)\).

Step 2: Translate the condition into an equation

The problem states that the \(y\) - coordinate is 10 less than the \(x\) - coordinate. So, we can write the equation as:
\[
y=x - 10
\]
This is the equation of a straight line with a slope of \(1\) and a \(y\) - intercept of \(-10\).

Final Answers

i. The equation of the set of points is \(\boldsymbol{y=-x + 2}\) (or \(\boldsymbol{x + y=2}\))
ii. The equation of the set of points is \(\boldsymbol{y=x - 10}\)