Answer:
<em>y = -2/3 x + 1</em>
Step-by-step explanation:
The line y = -2/3 x + 5 is in y = mx + b form, where m is the slope, so the slope of the given line is -2/3. Parallel lines have equal slopes, so the equation you are looking for also has slope -2/3.
The parallel line has equation
y = -2/3 x + b
We need to find b.
Since we are given a point, we substitute x and y with the x- and y-coordinates of the given point and solve for b. x = 6, and y = -3.
y = -2/3 x + b
-3 = (-2/3)(6) + b
-3 = -4 + b
1 = b
Now that we know b = 1, we can write the equation.
y = -2/3 x + b
y = -2/3 x + 1
