Question

find the slope-intercept form of the line passing through the point $(-6, -5)$ and parallel to the line $y=-2x+2$a $y=-2x-16$b $y=\frac{1}{2}x - 2$c $y=-2x-17$d $y=2x+17$2021. write the equation of the line that is parallel to $y=\frac{1}{3}x-3$ and passes through the point $(6, 2)$.2122. a line $l_1$ has slope $\frac{1}{4}$. state whether the line that passes through $(6,-5)$ and $(3, 7)$ is parallel or perpendicular to line $l_1$.2223. which best describes the relationship between the line that passes through $(9, -2)$ and $(5,0)$ and the line that passes through $(4, 8)$ and $(2, 4)$?a perpendicularb parallelc neither perpendicular nor parallel

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y=\frac{1}{3}x-3$, slope $m=\frac{1}{3}$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $m=\frac{1}{3}$, $(x_1,y_1)=(6,2)$:
$y-2=\frac{1}{3}(x-6)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y-2=\frac{1}{3}x-2$
$y=\frac{1}{3}x-2+2$
$y=\frac{1}{3}x$

Answer:

$y=\frac{1}{3}x$