Question

1. the point (1,6) lies on a line that has a rise of 4 and a run of 3. determine two more ordered pairs for each relationship.

for each relationship.
ints in any order that you prefer.

Explanation:

Step1: Find the slope

The slope \( m \) is given by \( \frac{\text{rise}}{\text{run}} \), so \( m = \frac{4}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(1,6) \) and \( m=\frac{4}{3} \).
So \( y - 6=\frac{4}{3}(x - 1) \).

Step3: Find the first new point

Let's find a point by increasing \( x \) by 3 (the run) and \( y \) by 4 (the rise) from \( (1,6) \).
New \( x = 1+3 = 4 \), new \( y=6 + 4=10 \). So one point is \( (4,10) \).

Step4: Find the second new point

Decrease \( x \) by 3 and \( y \) by 4 from \( (1,6) \).
New \( x=1 - 3=- 2 \), new \( y = 6-4 = 2 \). So another point is \( (-2,2) \).

Answer:

Two more ordered pairs are \((4,10)\) and \((-2,2)\) (answers may vary depending on the direction of rise and run, other valid points can be found by repeatedly applying the rise and run).