Which choice is the equation of a line that has a y-intercept of 7 and is parallel to the line represented by this equation?
y = 6x− 5
A. y = 6x+ 7
B. y = 6x− 7
C. y = -1/6x + 7
D. y = 1/6x + 7
the general equation is ... y = m x + b
m is the slope , b is the y-intercept
parallel lines have the same slope
thx ^.^
To determine which choice represents the equation of a line that is parallel to the given line, we need to understand the concept of parallel lines.
Two lines are parallel if they have the same slope and will never intersect.
The given equation is in the form y = mx + b, where m represents the slope of the line. In this case, the slope is 6.
To find a line parallel to the given line, we need to choose an equation that has the same slope and a different y-intercept.
The y-intercept of the given line is 7, so we need to look for an equation with the same slope of 6 and a different y-intercept.
Let's consider each option:
A. y = 6x + 7: This equation has the same slope of 6, but the same y-intercept of 7 as the given line. The line represented by this equation is actually the same line as the given line and not parallel to it.
B. y = 6x - 7: This equation has the same slope of 6, but a different y-intercept of -7. It satisfies the conditions for being parallel to the given line since it has the same slope but a different y-intercept.
C. y = -1/6x + 7: This equation has a slope of -1/6, which is not the same as the slope of the given line, so it is not parallel to it.
D. y = 1/6x + 7: This equation has a slope of 1/6, which is not the same as the slope of the given line, so it is not parallel to it.
Therefore, the correct answer is B. y = 6x - 7.