Question

select any two points shown on line a to draw a slope triangle. the line decreases from left to right. therefore, the slope is negative. enter the slope of line a: -1 enter a number to complete the equation for line a: y = -1x enter a number to complete the equation for line g: y = -1x + ( ) press the button to translate line a up 4 units.

Explanation:

Step1: Recall line - translation rule

The general form of a line 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 original line equation

The equation of line $a$ is $y=-1x + b$. To find $b$, we can use a point on the line. Let's assume the line $a$ passes through the origin $(0,0)$ (from the graph), substituting $x = 0$ and $y = 0$ into $y=-x + b$, we get $0=-0 + b$, so $b = 0$. The equation of line $a$ is $y=-x$.

Step3: Translate the line

We want to translate line $a$ up 4 units. Using the translation rule $y=mx+(b + k)$ with $m=-1$, $b = 0$ and $k = 4$, the equation of line $g$ is $y=-1x+4$.

Answer:

$y=-x + 4$