Question

select any two points shown on line u to draw a slope triangle. the line decreases from left to right. therefore, the slope is negative. enter the slope of line u: -1 enter a number to complete the equation for line u: y = -1 x press the button to translate line u down 5 units. enter numbers to complete the equation for line w: y = -1 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. Translating a line down by $k$ units changes the y - intercept. The original line $u$ has the equation $y=-1x + b$.

Step2: Apply the translation

If we translate the line $y = -x + b$ down 5 units, the new y - intercept $b$ becomes $b-5$. The slope remains the same because translation is a rigid transformation that does not change the steepness of the line. So the equation of line $w$ is $y=-1x+(b - 5)$. Since we are not given the original y - intercept of line $u$, assuming the original equation of line $u$ is $y=-x+0$ (for simplicity, as the original y - intercept value does not affect the translation rule for the purpose of finding the new equation), the equation of line $w$ is $y=-1x - 5$.

Answer:

$y=-1x - 5$