Question

select any two points shown on line r to draw a slope triangle. the line decreases from left to right. therefore, the slope is negative. enter the slope of line r: - 2/3. enter a number to complete the equation for line r: y=- 2/3x. press the button to translate line r up 5 units. enter numbers to complete the equation for line h: y = x+( )

Explanation:

Step1: Recall line - translation rule

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. If a line $y=mx + b$ is translated up $k$ units, the new equation is $y=mx+(b + k)$.

Step2: Identify the slope and y - intercept of line $r$

The equation of line $r$ is $y=-\frac{2}{3}x + b$. Let's assume the y - intercept of line $r$ is $0$ for simplicity (since no other information about it is given). So the equation of line $r$ is $y =-\frac{2}{3}x$.

Step3: Translate line $r$ up 5 units

Using the translation rule, when we translate the line $y =-\frac{2}{3}x$ up 5 units, the new equation of line $h$ is $y=-\frac{2}{3}x+5$.

Answer:

$y =-\frac{2}{3}x + 5$