Question

Which equation in slope-intercept form represents a line that passes through the point (6,−1) and is perpendicular to the line y=2x−7?

Answer 1

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It is the slope of the line

b: It is the cut point with the y axis

By definition, if two lines are perpendicular then the product of their slopes is -1.

If we have: $y = 2x-7$

$m_ {1} = 2\\2 * m 2 = - 1\\m_ {2} = - \frac {1} {2}$

Thus, the equation is of the form:

$y = - \frac {1} {2} x + b$

We substitute the point:

$-1 = - \frac {1} {2} (6) + b\\-1 = - \frac {1} {2} (6) + b\\-1 = -3 + b\\-1 + 3 = b\\b = 2$

Finally, the equation is:

$y = - \frac {1} {2} x + 2$

Answer:

$y = - \frac {1} {2} x + 2$