Question

Which equation could have been used to create this graph? y = 2x y = x + 4 y = 4x y = x + 2 A coordinate graph. The horizontal axis is labeled x and ranges from 0 to 10. The vertical axis is labeled y and ranges from 0 to 25. A line connects the points plotted at begin ordered pair 0 comma 0 end ordered pair, begin ordered pair 1 comma 4 end ordered pair, begin ordered pair 2 comma 8 end ordered pair, begin ordered pair 3 comma 12 end ordered pair, begin ordered pair 4 comma 16 end ordered pair, begin ordered pair 5 comma 20 end ordered pair, and begin ordered pair 6 comma 24 end ordered pair.

Answer 1

y =4x

Explanation:

points (0,0) (1,4) (2,8) (3,12) (4,16) (5,20) (6,24)

slope = (y2-y1)/(x2-x1)

= (4-0)/(1-0)

=4/1

= 4

the slope it 4

the y intercept is 0 ( where it crosses the y axis)

the slope intercept form of an equation is

y= mx+b

y = 4x+0

y =4x

Answer 2

Look at the picture.

The slope-intercept form:

`y=mx+b`

m - slope

b - y-intercept

From the graph wi have the y-intercept b = 0. Therefore the equation of a line is
`y=m+x`

The slope
`m=(\Delta y)/(\Delta x)`

`\Delta y=4,\ \Delta x=1\to m=(4)/(1)=4`

Answer: y = 4x.

We can calculate the slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have two points (0, 0) and (1, 4). Substitute:

`m=(4-0)/(1-0)=(4)/(1)=4`

`\boxed{y=4x}`