Question

Write an equation for the line that passes through the point ​(4,5​) and is perpendicular to−7x+y=2. Use​ slope-intercept form.

Answer 1

y= -1/7x + 39/7

Explanation:

Slope - intercept form is:

• y= mx +b, where m represents the slope of the line

Given the line:

• - 7x +y= 2,

which can be shown as:

• y= 7x+2 if we add 7x to both sides of equation

We need to write an equation for the line that it perpendicular to the given line and passes through the point (4,5)

As we know, perpendicular line has a slope opposite-reciprocal to the given, so the slope is:

• m= - 1/7

and the form of the line is:

• y= -1/7x +b

We can find b, by using the point (4, 5), which means x=4 and y=5:

• 5= -1/7 * 4 + b ⇒ b= 5+ 4/7= 5 4/7 = 39/7

And the equation for this line is:

• y= -1/7x + 39/7