Question

For the function whose graph is shown below which is the correct formula for the function

y= -x - 1
y= x + 1
y= -x + 1
y= x - 1

Answer 1

The slope is positive, as y is increasing as x goes towards the right.

The line crosses the y-axis at (0,1), so its y-intercept will be 1.

The answer is 'y= x + 1'.

Answer 2

Option B is correct.

y = x+1

Explanation:

Point slope form:

The equation of straight line is given by:

`y-y_1=m(x-x_1)` .....[1] where m is the slope of the line and a point
`(x_1, y_1)` lies on the line in the coordinate plane.

From the given graph:

Consider any two points i.e:

(0,1) and (-1, 0)

Calculate slope:

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

Substitute the given values we have;

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

Substitute the given values of m and (0, 1) in [1] we have;

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

y-1 = x

Add 1 to both sides we have;

y = x+1

Therefore, the function whose graph is shown below which is correct formula for the function is y = x+1