Given the equation:
y = 3x + 2
Let's find the equation that passes through the point (3, -1) and is parallel to the given line.
Apply the slope-intercept form of a linear equation:
y = mx + b
Where m is the slope and b is the y-intercept.
Now compare both equations:
y = mx + b
y = 3x + 2
This means the slope of the line m = 3.
y-intercept (b) = 2
The slope of parallel lines are equal.
Hence, the slope of the parallel line is also 3.
Now, let's find the y-intercept of the parallel line.
Given the point:
(x, y) ==> (3, -1)
Substitute 3 for x, -1 for y, then 3 for m in the slope-intercept equation to solve for b.
We have:
y = mx + b
-1 = 3(3) + b
-1 = 9 + b
Subtract 9 from both sides:
-1 - 9 = 9 - 9 + b
-10 = b
b = -10
The y-intercept of the parallel line is -10.
Therefore, the equation of the parallel line is:
y = 3x - 10
