Answer:
The gradient of the straight line that passes through (2, 6) and (6, 12) is [tex]m = \frac{3}{2}[/tex].
Step-by-step explanation:
Mathematically speaking, lines are represented by following first-order polynomials of the form:
[tex]y = b + m\cdot x[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m[/tex] - Slope.
[tex]b[/tex] - Intercept.
The gradient of the function is represented by the first derivative of the function:
[tex]y' = m[/tex]
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:
[tex]m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex] (2)
Where:
[tex]x_{A}[/tex], [tex]y_{A}[/tex] - Coordinates of point A.
[tex]x_{B}[/tex], [tex]y_{B}[/tex] - Coordinates of point B.
If we know that [tex]A(x,y) = (2,6)[/tex] and [tex]B(x,y) = (6,12)[/tex], then the gradient of the straight line is:
[tex]m = \frac{12-6}{6-2}[/tex]
[tex]m = \frac{6}{4}[/tex]
[tex]m = \frac{3}{2}[/tex]
The gradient of the straight line that passes through (2, 6) and (6, 12) is [tex]m = \frac{3}{2}[/tex].
