which equation represents a line parallel to the line given by y-3x=6?
A. y= -3x+4
B. y= 3x-2
C. y= 1/3x+6
D. y= -1/3x+4
The standard equation for a line is:
y = mx + b
where
m = the slope of the line
b = the y intercept
putting y - 3x = 6 in standard form:
y = 3x + 6
Therefore the slope of the line is 3. For lines to be parallel, the slope must be the same. Which of the possible answers has the same slope?
To determine which equation represents a line parallel to the given line, we need to compare the slopes of the lines.
The given line has the equation: y - 3x = 6.
To find the slope of this line, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope:
y - 3x = 6
Add 3x to both sides:
y = 3x + 6
Comparing this equation to y = mx + b, we see that the slope (m) of the given line is 3.
To find a line parallel to this, we need to look for an equation with the same slope of 3.
Let's check the options:
A. y = -3x + 4: This equation has a slope of -3, not 3. It is not parallel to the given line.
B. y = 3x - 2: This equation has a slope of 3. It is parallel to the given line.
C. y = (1/3)x + 6: This equation has a slope of 1/3, not 3. It is not parallel to the given line.
D. y = -1/3x + 4: This equation has a slope of -1/3, not 3. It is not parallel to the given line.
Therefore, the line parallel to the given line is represented by equation B. y = 3x - 2.