Equation of the line in slope-intercept form

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

To solve this question, you need to know (1) how to use the point-slope form of a line (which is used whenever you are given two points or a point and a slope):

y - y₁ = m ( x - x₁ ) OR y = m ( x - x₁ ) + y₁ where m is the slope and (x₁, y₁) is the point on the new line

(2) How to find the slope of a line perpendicular to another line - the slopes of perpendicular lines are negative inverses and obey the rule: m₁ * m₂ = -1 which can also be written as:

m₂ = - 1/m₁

(3) how to rearrange the equation into slope intercept form.

(4) the parts of slope-intercept form: y = mx + b where m is the slope and b is the y-intercept (the point (0, b))

The given line, y = 3x - 5, has a slope m₁ = 3. Using the relationship between the slopes of parallel lines, give the slope of the new line: m₂ = -1/m₁ = - 1/3

This slope and the given point (0,7) can be substituted into the point slope form of a line OR we can use the fact that the given point is the y-intercept of the new line (the y-intercept is the value of y when x = 0) and get y = (-1/3)x + 7

Answer 2

slope of the given line is 3

perpendicular line has slope (-1/3)

B = y - mx

= 7 - (-1/3)(0)

= 7

y = (-1/3)x + 7