Question

What is the equation of the line, in slope-intercept form, that passes through the point (0,7) and is perpendicular to the line y=3x−5?

Answer 1

Answer:

=12

Step-by-step explanation:

7=3(0)-5

7=-5

7+5

=12

Im pretty sure this is the answer

Answer 2

Answer:

$y=-\frac{1}{3}x+7$

Step-by-step explanation:

The slope-intercept form is: $y=mx+b$; where m is the slope, and b is the y-axis interception.

So, the problem is asking for a line that it's perpendicular to $y=3x-5$. This perpendicular relation means that the line we have to find have an inverse and opposite slope than the given line, that's expressed like this:

$m_{1}m_{2}=-1$

That expression is the condition to have perpendicular lines. So, the given line has a slope of 3, now we can find the slope of the new line:

$m_{1}m_{2}=-1\\m_{1}=\frac{-1}{m_{2}}=-\frac{1}{3}$

Now we have the slope of the new perpendicular line, we use the point-slope formula to find its equation:

$y-y_{1}=m(x-x_{1})\\ y-7=-\frac{1}{3}(x-0)\\y=-\frac{1}{3}x+7$

Therefore, the slope-intercept form of the new perpendicular line is:

$y=-\frac{1}{3}x+7$