Question

A function f(x) is graphed.

What is the slope of the function? M= 1,2,3,4
What is the y-intercept of the function? B= -2,-1,1,2
Which equation represents the graph of the function y=-x+2 , y=x+2 , y=2x+1 , y=-2x+1

Answer 1

2

1

y = 2x + 1

Explanation:

Answer 2

Point-Slope form: The equation of line is given by:

`y-y_1=m(x-x_1)` ......[1]

where m is the slope and
`(x_1,y_1)` is the point on the line.

From the given graph:

Consider two points i.e,

`(0, 1)` and (-0.5, 0)

Calculate slope:

Formula for slope is given by;

`\text{Slope}(m) = (y_2-y_1)/(x_2-x_1)`

Substitute the given values we have;

`m = (0-1)/(-0.5-0) = (-1)/(-0.5) = (10)/(5) =2`

Now, substitute the value of m = 2 and (0, 1) in equation [1] we have;

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

y-1 = 2x

Add 1 to both sides we get;

y = 2x+1

On comparing equation y = 2x+1 with the slope intercept form of a line (i.e, y = mx+b) then we have;

slope(m) = 2

y-intercept(b) = 1

therefore, the slope of the function:

m = 2

y-intercept(b) = 1

and the equation represents the graph: y = 2x+1