Questions: Suppose you begin at a point on a line with slope m and move h units in the x-direction. How many units must you move in the y-direction to return to the line? m=3, h=0.20 You must move units in the y-direction to return to the line. (Simplify your answer.)

Suppose you begin at a point on a line with slope m and move h units in the x-direction. How many units must you move in the y-direction to return to the line?

m=3, h=0.20

You must move units in the y-direction to return to the line. (Simplify your answer.)

Transcript text: Suppose you begin at a point on a line with slope $m$ and move $h$ units in the $x$-direction. How many units must you move in the $y$-direction to refurn to the line? \[ m=3, h=0.20 \] You must move $\square$ units in the $y$-direction to return to the line. (Simplify your answer.)

Solution

Solution Steps

Step 1: Understand the problem

We are given a line with slope $ m = 3 $. Starting from a point on this line, we move $ h = 0.20 $ units in the $ x $-direction. We need to determine how many units to move in the $ y $-direction to return to the line.

Step 2: Use the slope formula

The slope $ m $ of a line is defined as the change in $ y $ divided by the change in $ x $: \[ m = \frac{\Delta y}{\Delta x} \] Here, $ \Delta x = h = 0.20 $, and $ m = 3 $. We need to solve for $ \Delta y $: \[ 3 = \frac{\Delta y}{0.20} \]

Step 3: Solve for $ \Delta y $

Multiply both sides of the equation by $ 0.20 $ to isolate $ \Delta y $: \[ \Delta y = 3 \times 0.20 = 0.60 \]