Question

Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=-3x+2

Answer 1

To find the equation of a line perpendicular to another line, we determine the slope of the original line and find the negative reciprocal of that slope. The equation of the line passing through the point (3,5) and perpendicular to y = -3x + 2 is y = 1/3x + 4.

Step-by-step explanation:

To find the equation of a line perpendicular to another line, we need to determine the slope of the original line and then find the negative reciprocal of that slope. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. In the given equation, y = -3x + 2, the slope is -3. The negative reciprocal of -3 is 1/3, so the perpendicular line has a slope of 1/3. We also know that the line passes through the point (3,5), so we can use the point-slope form of a line to find the equation.

Using the point-slope form, y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope, we have:

y - 5 = 1/3(x - 3)

Expanding and simplifying:

y - 5 = 1/3x - 1

y = 1/3x + 4

Therefore, the equation of the straight line passing through the point (3,5) and perpendicular to the line y = -3x + 2 is y = 1/3x + 4.

Answer 2

y =
`(1)/(3)` x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - 3x + 2 is in this form with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-3)` =
`(1)/(3)`

y =
`(1)/(3)` x + c ← is the partial equation

to find c substitute (3, 5 ) into the partial equation

5 = 1 + c ⇒ c = 5 - 1 = 4

y =
`(1)/(3)` x + 4 ← equation of perpendicular line