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solniwko [45]
2 years ago
13

Find the point on the line y = 2x + 3 that is closest to the origin.

Mathematics
1 answer:
ch4aika [34]2 years ago
3 0
1)We have to make a line perpendicular to y=2x+3, passing through the point (0,0).

y=2x+3   
m=solpe=2

The slope of the line perpedicular to y=2x+3 is m´
m´=-1/m
m´=-1/2

Point slope form:
y-y₀=m(x-x₀)
(0,0)
m=-1/2

y-0=-1/2(x-0)
y=-x/2

Therefore, the line perpendicular to y=2x+3 is y=-x/2.

2)The point on the line y=2x+3 tha is closest to the origin is the point of intersection of the two lines.

y=2x+3
y=-x/2

We can solve this system of equations by equalization method.
2x+3=-x/2
least common multiple=2
4x+6=-x
4x+x=-6
5x=-6
x=-6/5  (=-1.2)

y=-x/2
y=-(-6/5)/2=6/10=3/5    (=0,6)

Therefore: the point of the line y=2x+3 that is closest to the origin is:
 (-1.2 , 0.6)

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Answer:

24

Step-by-step explanation:

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2 years ago
write a linear equation that intersects y=x^2 at two points. Then write a second linear equation that intersects y=x^2 at just o
Liula [17]

We know that y = x^2 is a parabola, concave up, with vertex in the origin (0,0)

So, we may use three horizontal lines for our purpose: any horizontal line above the x axis will intersect the parabola twice. The x axis itself intersects the parabola once on the vertex, while any horizontal line below the x axis won't intercept the parabola.

Here's the examples:

  • The horizontal line y = 4 intercepts the parabola twice: the system y = x^2,\ y = 4 is solved by x^2=4 \implies x = \pm 2
  • The horizontal line y=0 intercepts the parabola only once: the system is y=x^2,\ y=0 which yields x^2=0\implies x=0 which is a repeated solution
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5 0
3 years ago
Your friend is graphing the point (4, 3). She plans to start at the origin and go up 4 spaces. Which statement about her method
goldfiish [28.3K]
The true statement about her method would be to start at the origin. But you would go up 4 spaces you would go to the right 4 spaces.
7 0
2 years ago
Read 2 more answers
Please help me with this question!!!
scoundrel [369]
First calculate the slope by change in y over change in x
it’s -0.334
then find y intercept
-6

so all together
-0.334x-6
5 0
3 years ago
A cable company offers two movie plans. Plan A costs $120 per month plus $5 per movie. Plan B costs $150 per month for unlimited
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Answer: he could watch a maximum of 6 movies with plan A and still pay the same but the better deal is plan B. I hope that this helps! :)

Step-by-step explanation:

6 0
2 years ago
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