given the equation x+3y=7, what is the perpendicular line passing through (0,1)?

Question

given tge equation x+3y=7 what is tge perpendicular line passing through 0,1?

Answer 1

x+3y=7; written in the slope intercept form will be

y= -(1/3)x + (7/3) where the slope will be -1/3 then the slope of the perpendicular line to this line will be 3.

writing the new equation in the point slope form we have

(y-1) = 3(x-0)

the equation will be:

y = 3x + 1

 

 

Answer 2

To identify the slope of given line you need to rewrite it in the slope-intercept form y = mx + b where m is a slope and b is a y-intercept of the line.

To do that move x to the right side then divide each term of equation by 3.

You will get  y = -1/3x + 7/3

From this form of linear equation we can see that the slope for this line is -1/3.

The slopes of perpendicular lines are opposite reciprocals (opposite sign, flipped fraction). 

So, the slope of perpendicular line is equal to 3. 

Given point (0, 1) is a y-intercept  because x-coordinate is equal to 0.

So m=3 and b=1.

Therefore the equation of the perpendicular line will be y = 3x + 1.