please help me with this math question?

Question

Write an equation of a line that is perpendicular to y = 2x + 3 and
passes through (3,4).

how do you guys get these answers?...do you solve them by yourselfs or do u use a website?

Answer 1

perpendicular lines have opposite and inverse slopes so the slope of your new line is -1/2.

y = (-1/2)x + c

Plug in the point (3,4) for x and y to find c.

4 = -3/2 + c
11/2 = c

So your perpendicular line is:

y = (-1/2)x + 11/2

Edit: I solved it myself.

Answer 2

for the equation y = 2x + 3, the equation is already in slope intercept form. (y = mx + b where m is the slope and b is the y intercept) so we know that the slope of that line is 2.

two lines that are parallel have the same slope
two lines that are perpendicular have slopes that are negative reciprocals of each other.

Since the we want a line perpendicular to one with a slope of 2, we want the new line to have a slope of -1/2

so the new line would be y = -1/2x + b
to solve for the correct b, you plug in the x and y point that the line is supposed to pass through, (3, 4)

so 4 = -1/2(3) + b
4 = -3/2 + b
11/2 = b

so your new line in slope intercept form is y = -1/2x + 11/2

Answer 3

Gradient of given line is 2.
Gradient of perpendicular line is (-1/2)
Perpendicular passes thro` point (3,4) and equation is given by:-
y - 4 = (-1/2).(x - 3)
y - 4 = (-1/2).x + 3/2
y = (-1/2).x + 11/2

Information and examples re straight lines may be had from standard school text books all over the world.

Answer 4

It is easy.the eq.is modified like this..2x-y+3=0
equationof a perpendicular st.line is bx-ay+c=0.
For this line it is x+2y+c=0.
it passes through (3,4)
so apply it.
And the equation becomes 3+2(4)+c=0
so 3+8+c = 0.
and so c= -11.
therefore the eqution of the line is x+2y-11=0
i.e.,x+2y=11.

The key point for this sum is the formula.
Remember equation of a st. line perpendicular to a line with equation ax+by+k=0 is bx-ay+c=0.

ALL THE BEST.

Answer 5

y=-2x+b
4=-2(3)+b
4=-6+b
4+6=b
10=b
y=-2x+10

1) You want a perpendicular line, so try the negative slope...and then substitue x and y with your coordinates. Then, solve for B. (3,4) does go through the line, and does intersect.

Answer 6

(the slope of a line perpendicular to the line) multiplied by (the slope of the line) equals -1, so:

the slope of the given line is: 2 call this m1

call the slope of the perpendicular line m2

so 2 * m2 = -1

so m2 = -1/2

now just plug into the point-slope forn to get:

(y-4) = -1/2 (x-3)

Your teacher might want the final answer in slope-intercept form, so here it is:

2(y-4) = -(x-3)

2y - 8 = -x - 3

2y = -x + 5

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

Answer 7

y = 2x + 3

so the slope of this line is m = 2
the slope of line perpendicular this line is m = -1/2

if it passes through (3,4) therefore

(y - y1) = m (x - x1)

(y - 4) = -(1/2)(x - 3)

2y = -x + 11

Answer 8

Y=5x+3?

Answer 9

slope of given line=m1=2
slope of line perpendicular to this= -1/2

equation of reqd line
(y-4)= -1/2(x-3)
2y-8= -x+3
2y+x=11

therefore,reqd equation is
2y+x=11

Answer 10

y - 4 = (-1/2)(x-3), in point-slope form
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Reason: (-1/2)(2) = -1. If one slope is 2, then the other one must be -1/2 if the two lines are perpendicular to each other.