Given the linear equation 5y = -3x + 19, find
(a) the slope of a line perpendicular to the given line.
(b) the slope of a line parallel to the given line.
A. (a) -5/3 (b) 3/5
B. (a) -3/5 (b) 5/3
C. (a) 5/3 (b)-3/5
D. (a) 3/5 (b)-5/3
Rewrite the equation as:
y=(-3/5)x + 19/5
which makes the slope as (-3/5)
Lines that are parallel have the same slope.
Two lines that are perpendicular to each other have the product of the slope equal to -1.
That should be enough for you to make the right choice.
To find the slope of a line perpendicular to the given line, we need to know that perpendicular lines have slopes that are negative reciprocals of each other.
The given equation is in the form of y = mx + b, where m represents the slope. To find the slope of the given line, we first need to rearrange the equation in slope-intercept form.
5y = -3x + 19
Divide both sides by 5:
y = (-3/5)x + 19/5
From this equation, we can see that the slope of the given line is -3/5.
To find the slope of a line perpendicular to this, we take the negative reciprocal of -3/5, which is 5/3.
Therefore, the slope of a line perpendicular to the given line is 5/3.
Now, to find the slope of a line parallel to the given line, we know that parallel lines have the same slope.
Therefore, the slope of a line parallel to the given line is also -3/5.
Hence, the answer is B. (a) -3/5 (b) 5/3.