Question

line sp is represented by the equation y = -x - 14. determine the equation, in slope - intercept form, of the line fj that is parallel to line sp and passes through the point f(-6,0).

Explanation:

Step1: Identify the slope of line SP

The equation of line SP is $y=-x - 14$, which is in the form $y = mx + b$ where $m$ is the slope. So the slope of line SP, $m=-1$. Since parallel lines have equal slopes, the slope of the line we want to find is also $m=-1$.

Step2: Use the point - slope form to find the equation

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. The line passes through the point $F(-6,0)$. Substitute $x_1=-6$, $y_1 = 0$ and $m=-1$ into the point - slope form:
$y-0=-1(x - (-6))$
$y=-x - 6$

Answer:

$y=-x - 6$