Verified Answer :

You need to calculate it's slope.
(x₁,y₁) = (2,8) and (x₂,y₂) = (4,12)
Now,(y₂-y₁) = m(x₂-x₁)
(12-8) = m(4-2)
2m = 4
m = 4/2
m = 2

Now, take any one point for calculation of b in equation;
8 = 2(2) + b
b = 8 - 4
b = 4

So, Equation of the line would be: y = 2x + 4 

In short, Your Answer would be Option C

Hope this helps!

Lanuel

The equation which best represents the line with the given points (2, 8) and (4, 12) is \(y = 2x + 4\).

Given the following points:

  • Points on the x-axis = (2, 8).
  • Points on the y-axis = (4, 12).

To determine the equation which best represents the line, we would find its slope by using the following formula:

The slope of a line refers to the gradient of a line and it is typically used to describe both the direction and steepness of an equation of a straight line.

Mathematically, the slope of a line is given by the following formula;

\(Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substituting the given points into the formula, we have;

\(Slope. \;m = \frac{12 - 8}{4 - 2}\\\\Slope. \;m = \frac{4}{2}\)

Slope, m = 2.

The standard form of an equation of line is given by the formula;

\(y = mx + c\)

Where:

  • x and y are the points.
  • m is the slope.
  • b is the intercept.

Next, we would solve for the intercept:

\(y = mx + b\\\\8 = 2(2) + b\\\\8 = 4 + b\\\\b = 8 - 4\)

Intercept, b = 4.

Finally, we can now write the equation which best represents the line as follows:

\(y = 2x + 4\)

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