Please help with a X-intercept question?

Question

The x-intercept of the line through the point (2,7) which is perpendicular to the line through the points (11,2) and (14,3) is:

a) A positive number
b) A negative number
c) zero
d) none of the above

First I found the slope for (11,2) (14,) m=1/3
then placed it in y intercept form. Then I got lost.


I think the answer is positive but I'm not sure if my work is correct.

Please help me.

Answer 1

you need to find the slope for (11,2) and (14,3) first:
m= (3-2) / (14-11) = 1/3

the reciprocal of 1/3 is -3 which is the slope of the second equation.

y=mx+b
7= -3(2)+b
7=-6+b
b= 13

y=-3x+13

to figure out the x-int, you need to plug in 0 for y.

0= -3x+13
-13= -3x
x= 13/3

x-int is positive.

Answer 2

There is no reason for you to get lost. This is not a forest of questions.

When you have the slope of the given line, you can easily figure out the slope of the perpendicular line to it, because the one slope multiplied by the other slope is equal to -1. Therefore the slope of the line through the point (2,7) is -3. Let us assume the equation of this line as

y = mx + c, where m is the slope and c is the y-intercept.

Since we know the slope we can write
y = -3x + c

Since this line passes through (2, 7), we have 7 = -3 * 2 + c, that is c = 13.
Now the equation of the line becomes
y = 3x + 13

We know that at the x-intercept y = 0. Substitute this value in the above equation and you get the x-intercept;

0 = -3x + 13, i.e. x = 13/3

The answer is "A Positive Number"

Answer 3

Slope of line is 1/3 is correct. Now take negative reciprocal and get -3 which is the slope of the line that is perpendiclar to it.

So y = -3x+ b
Since the line goes through (2,7) we have
7 = -3(2) + b, so b = 13.
The line is y= -3x + 13
Its x- intercept occurs when y = 0 so
0 = -3x + 13
x= 13/3 which is a positive number.

Answer 4

slope of line through (11,2) and (14,3) is
m=(2-3)/(11-14)=-1/-3=1/3

the line perpindicular to this has a slope of -1/(1/3)=-3

y=-3x+6
includes point (2,7)
7=-3*2+b
b=13
y=-3x+13 to find the x-intercept set y=0
0=-3x+13
3x=13
x=13/3=4 1/3

a) A positive number is correct

Answer 5

m = (3-2)/(14-11) = 1/3
if two lines are perpendicular then m * m' = -1 so m' = -3
then you'll have the equation
y = -3x + b
(2,7) is on that line so we get 7 = -6 + b so b=13
y = -3x + 13
so the x intercept is
0 = -3x + 13
x = 13/3

the answer is a) positive

Answer 6

m (of the perpendicular line) = (3-2) / (14-11)
m (perpendicular) = 1/3

m (this line) = -1/m(perpendicular) = -1/(1/3) = -3

y = -3x+b is the general form. Put in the point they give you (2,7) and you get

7=-3(2)+b
7=-6+b
b=13
y=-3x+13
Now, put in 0 for y to solve for the x-intercept
0=-3x+13
3x=13
x=13/3

answer is A

Answer 7

y = mx + b

once you know the slope, plug in one of the coordinate pairs for x and y and the slope m. b will then be left as the intercept.