Answer:
c. 3y - x = 10
Explanation:
The slope-intercept form of a line
The equation of the line in the slope-intercept form is:
y = mx + b
Here, m the slope and b the y-intercept.
To compare the slope of different lines, we should write them in the above form and compare their values of m.
The given line is:
y = 3x + 9
The slope of this line is m=3
Any parallel line must have the very same value of m.
None of the following options can be directly compared because they are not in the slope-intercept form, so they must be converted.
a. 3x - y = 10
Solving for y:
- y = 10 -3x
y = 3x - 10
The slope of this line is m=3, thus this line is parallel to the given line
c. 3y - x = 10
Solving for y:
3y = x + 10
y = 1/3 x - 10
The slope of this line is m=1/3, thus this line is NOT parallel to the given line
b. y - 3x = 11
Solving for y:
y = 3x + 11
The slope of this line is m=3, thus this line is parallel to the given line
d. 6x - 2y = 10
Solving for y:
- 2y = -6x + 10
Dividing by -2:
y = 3x - 5
The slope of this line is m=3, thus this line is parallel to the given line
Answer: c. 3y - x = 10