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
the other two answers pertain to perpendicular lines, so i excluded them. i was going to select B, but i'm unsure if that is correct.
thank you! :)
The y intercept is the value of y when x = 0 so it is indeed A
To determine which choice represents the equation of a line that is parallel to the given line and has a y-intercept of 7, we need to recall the properties of parallel lines.
Two lines are parallel if they have the same slope. The equation of the given line is y = 6x - 5. This equation is in slope-intercept form, y = mx + b, where m represents the slope. So, we know that the slope of the given line is 6.
Since we want to find an equation of a line that is parallel, the slope of the new line must also be 6. Additionally, it should have a y-intercept of 7. Let's analyze the answer choices:
A. y = 6x + 7
B. y = 6x - 7
Comparing the slopes, both options have a slope of 6, which satisfies the requirement of parallel lines. Now, let's consider the y-intercepts:
In option A, the y-intercept is 7, which satisfies the given requirement.
In option B, the y-intercept is -7, which does not satisfy the given requirement.
Thus, the correct choice is A. y = 6x + 7, since it represents a line with a y-intercept of 7 and is parallel to the given line.