Question

A function is represented by the graph.

Complete the statement by selecting from the drop-down menu.
greater than

lessthan

equal to

The y-intercept of the function​ ​ y=3x+2 ​ ​​is the y-intercept of the function represented in the graph.

Answer 1

equal to >>>>>>>>>>>>>>>>>>>>>>>>>

Answer 2

'Equal to' is the answer.

Explanation:

The equation of a straight line is given by y=mx+c, where m= slope and c= y-intercept.

In the given equation y=3x+2, the y-intercept is 2.

Now, from the graph we get two pair of points (0,2) and (-1,0). Using these points, we will find the slope.

i.e.
`m = (y_(2)-y_(1))/(x_(2) -x_(1))`

i.e. m=
`(0-2)/(-1-0)`

i.e. m= 2.

Now, using this slope and the point (-1,0) in the given equation, we will find the equation of the graph.

i.e. (y-
`y_(1)`) = m*(x-
`x_(1)`)

i.e y-0 = 2*(x-(-1))

i.e. y= 2*(x+1)

i.e. y= 2x+2

Therefore, y=2x+2 is the equation of the graph and comparing with the general form at the start, the y-intercept is 2.

Hence, both equations have equal y-intercept.