What is the equation of the line, in slope-intercept form, that passes through the point (4, -1) and is perpendicular to the line whose equation is 2x - y - 7 = 0?

y = -1/2x + 1
y = 1/2x - 1
y = 2x + 1

Question

What is the equation of the line, in slope-intercept form, that passes through the point (4, -1) and is perpendicular to the line whose equation is 2x - y - 7 = 0? 



y = -1/2x + 1
y = 1/2x - 1
y = 2x + 1

oaktree · Answer

Hi again. Like last time, we're going to want to start with the slope. So what's the slope of the line we're given?

oaktree · Answer

@mjcobb2, do you know the slope of the line given?

anonymous · Answer

No

oaktree · Answer

Okay then. So first we want to put it in slope-intercept form, which is y=2x-7. So the slope is 2. However, since the line we want is perpendicular, the slope of our line is the opposite reciprocal of 2, which is -1/2. So our slope is -1/2.

For the next phase, we plug the slope and the point given into the slope-intercept formula, and we get $$-1 = \frac{ -1 }{ 2 } \times 4 + b$$Which yields b = -3. So our line is $$y = \frac{ -1 }{ 2 } x -3$$

oaktree · Answer

Which, in the form you asked for last question, is the same as $$x + 2y + 6 = 0$$

anonymous · Answer

Thank you very much I am taking a test and it is very hard as I really don't like these kind of questions...

oaktree · Answer

No problem.