Question

Write an equation in slope intercept form of the line that passes through (4,-4) and (8,4)

Answer 1

Answer:

y = 2x - 12

Step-by-step explanation:

To write the equation of the line in slope intercept form, we need to determine the slope of the line and the y-intercept of the line. Once we determine the slope and the y-intercept of the line, we can substitute them into the slope intercept equation to determine the equation of the line.

Question: How to determine the slope and the y-intercept?

The slope of the line can be determined by applying the slope formula and the y-intercept can be determined by substituting the "determined slope" and any point whereas the line passes through that point, into the slope intercept form equation.

[Step-1] Finding the slope of the line:

The formula that can be used to find the slope of a line are as follows:

$\underline{\text{Slope of a line}:} \ \boxed{\frac{y_{2} - y_1 }{x_2 - x_1} }$

Let us substitute (4, -4) and (8, 4) into the slope formula by substituting into their respective places. As a result, the slope will be as follows:

$\implies \dfrac{4 - (-4)}{8 - 4} = \dfrac{4 + 4}{4} = \dfrac{8}{4} = 2$

Therefore, the slope is 2.

[Step-2] Finding the y-intercept of the line:

According to the instruction stated above, we have to substitute the slope of the line and the x/y coordinates of any point, whereas the line passes through that point, into the slope intercept form equation.

$\implies \text{y = mx + b (Slope intercept form equation)}$

Slope is usually known as "m" in the slope intercept form equation and y-intercept is usually known as "b" in the slope intercept form equation.

Therefore, we have: $m = 2$

$\implies \text{y = (2)x + b}$

Further, let us substitute the coordinate of any point, whereas the line intersects that point. I will choose the point [8, 4].

Now, let us expand the coordinate (8, 4) to determine the x and y coordinates. Since we have 8 as the x-coordinate and 4 as the y-coordinate, we can say that: x = 8; y = 4

$\implies \text{(4) = (2)(8) + b}$

Then, let us solve for b. The value of "b" will be the y-intercept.

$\implies \text{4 = 16 + b}$

$\implies \text{4 - 16 = \boxed{-12 = b}}$

Therefore, the y-intercept is -12.

[Step-3] Determining the equation of the line

According to the instruction stated above, we have to substitute the slope and the y-intercept of the line in the slope intercept form equation to determine the equation of the line in slope intercept form.

$\implies y = mx + b \longrightarrow \text{Slope intercept form}$

$\implies y = (2)x + (-12)$

Finally, simplify the equation:

$\implies y = 2x -12$

Therefore, the equation of the line in slope intercept form is y = 2x - 12.

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