which of the following lines is perpendicular to the line y=-3/5x+1
a.3x+5y=10
b. 3x-5y=20
c.5x+3y=21
d. 5x-3y=27
To determine which line is perpendicular to y = -3/5x + 1, we need to find the line with a slope that is the negative reciprocal of -3/5.
The negative reciprocal of -3/5 is 5/3.
Thus, the line we seek must have a slope of 5/3.
Now, let's examine the options:
a. 3x + 5y = 10
To determine the slope, let's rewrite the equation in slope-intercept form:
5y = -3x + 10
y = -3/5x + 2/5
The slope of this line is -3/5, not the reciprocal of 5/3. Therefore, it is not perpendicular to the given line.
b. 3x - 5y = 20
To determine the slope, let's rewrite the equation in slope-intercept form:
-5y = -3x + 20
y = 3/5x - 4
The slope of this line is 3/5, not the reciprocal of 5/3. Therefore, it is not perpendicular to the given line.
c. 5x + 3y = 21
To determine the slope, let's rewrite the equation in slope-intercept form:
3y = -5x + 21
y = -5/3x + 7
The slope of this line is -5/3, which is the reciprocal of 5/3. Therefore, it is perpendicular to the given line.
d. 5x - 3y = 27
To determine the slope, let's rewrite the equation in slope-intercept form:
-3y = -5x + 27
y = 5/3x - 9
The slope of this line is 5/3, which is the reciprocal of 5/3. Therefore, it is perpendicular to the given line.
In conclusion, both options c (5x + 3y = 21) and d (5x - 3y = 27) are lines perpendicular to y = -3/5x + 1.