Question

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

Answer 1

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

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