95,463 views
28 votes
28 votes
Write an equation for line L in point-slope form and

slope-intercept form.
L is perpendicular to y = 2x.
6
-2
6
15
y = 2x
(12)
2
50
Write an equation for line L in point-slope form.
(Simplify your answer. Use integers or fractions
for any numbers in the equation.)

Write an equation for line L in point-slope form and slope-intercept form. L is perpendicular-example-1
User Sunteen Wu
by
2.6k points

1 Answer

14 votes
14 votes

Explanation:

the line is perpendicular to

y = 2x.

and it goes through the point (1, 2).

the point-slope form looks like

y - y1 = a(x - x1)

"a"being the slope, and (x1, y1) being a point on the line.

the slope-intercept form is

y = ax + b

"a" is again the slope, "b" is the y-intercept (the y value when x = 0).

as you can see, we need the slope of the new line in both cases.

then we will start with the point-slope form, and transform it into the slope-intercept form.

the slope of a line is generally the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

it is always the factor of x.

we can see it is 2 for the original line. that means 2/1.

a perpendicular slope is turning the x and y values upside down, and is flipping the sign.

so, in our case it is

-1/2

so, starting with the new slope and the point to create the point-slope form :

y - 2 = -1/2 × (x - 1)

and from there we transform into the slope-intercept form :

2y - 4 = -x + 1

2y = -x + 5

y = (-x + 5)/2 = -1/2 x + 5/2 = -1/2 × (x - 5)

all of the expressions in the last line are valid forms to write it.

User Xelber
by
2.8k points