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3 years ago

Graph y=x, y=2x, and y=3x on the same coordinate plane. How are the graphs alike? How are they different? Compare the slopes.

Mathematics

2 answers:

grigory [225]3 years ago

4 0

Answer:

Step-by-step explanation:

Ne4ueva [31]3 years ago

3 0

Answer:

all the three graphs passes through the origin (0,0)

the slope of the lines are different.

for y=x equation , slope =1

for y=2x equation slope = 2

for y=3x equation slope = 3

Step-by-step explanation:

LEts graph all the three equations

y=x , y=2x, y= 3x

Make a table for each equation and find two points

x y=x x y= 2x x y=3x

0 0 0 0 0 0

1 1 1 2 1 3

Graph is attached below

From the graph we can see that , all the three graphs passes through the origin (0,0)

From the graph we can see that the steepness of the line changes for each line. steepness of the line is noting but the slope . So the slope of the lines are different.

Given equation is in the form of y=mx+b

m is the slope

for y=x equation , slope =1

for y=2x equation slope = 2

for y=3x equation slope = 3

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guapka [62]

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Explanation:

When you draw the situation you find two triangles.

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d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x

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b) distance between the helicopter and the elementary school = hypotenuse

c) opposite-leg to angle 62° = height of the helicopter

d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x

3) tangent ratios

a) triangle with the helicpoter and the high school

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b) triangle with the helicopter and the elementary school

tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°

c) equal the height from both triangles:

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x tan 20° = 5 tan 62° - x tan 62°

x tan 20° + x tan 62° = 5 tan 62°

x (tan 20° + tan 62°) = 5 tan 62°

⇒ x = 5 tant 62° / ( tan 20° + tan 62°)

⇒ x = 4,19 miles

=> height = x tan 20° = 4,19 tan 20° = 1,525 miles

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