Work out the gradient of the straight line that passes through (2,6) and (6,12)

The gradient of the straight line that passes through (2, 6) and (6, 12) is .

Step-by-step explanation:

Mathematically speaking, lines are represented by following first-order polynomials of the form:

(1)

Where:

- Independent variable.

- Dependent variable.

- Slope.

- Intercept.

The gradient of the function is represented by the first derivative of the function:

Then, we conclude that the gradient of the staight line is the slope. According to Euclidean Geometry, a line can be form after knowing the locations of two distinct points on plane. By definition of secant line, we calculate the slope:

(2)

Where:

, - Coordinates of point A.

, - Coordinates of point B.

If we know that and , then the gradient of the straight line is:

The gradient of the straight line that passes through (2, 6) and (6, 12) is .

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.