Mathematics, 29.01.2022 04:40 ayoismeisalex

determine the equation of the line that intersects the y-axis at(0,8) and intersects X-axis at (8,0) PLZ HELP

determine the equation of the line that intersects the y-axis at(0,8) and intersects X-axis at (8,0

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Answer from: gamerella101

B: y = -x + 8

Step-by-step explanation:

The given problem requires us to determine the equation of the line that passes through the y-axis at point (0, 8) and the x-axis at point (8, 0).

Definitions:

The y-intercept is the point on the graph where it crosses the y-axis. It is also the value of "y" when x = 0.

The x-intercept is the point on the graph where it crosses the x-axis. It is also the value of "x" when y = 0

Solve for the slope:

We can use the two pairs of coordinates to find the slope of the line using the following slope formula:

$\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}$

We will use the following points to solve for the slope:

(x₁, y₁) = (0, 8) ⇒ This is the y-intercept of the line. (x₂, y₂) = (8, 0) ⇒ This is the x-intercept of the line.

Substitute these points into the slope formula:

$\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}\:=\:\frac{0-8}{8-0}\:=\:\frac{-8}{8}\:=-1}$

Therefore, the slope of the line is -1.

Y-intercept:

As explained in the previous sections of this post, the y-intercept is (0, 8). Its y-coordinate is the value of the y-intercept (b) in the slope-intercept form, y = mx + b.

⇒ Hence, the y-intercept of the equation is: b = 8.

Linear Equation in Slope-intercept Form:

Now that we have our values for the slope, m = -1, and the y-intercept, b = 8, we can plug these values into the slope-intercept form:

⇒ y = -1x + 8 or simply, y = -x + 8.

Double-check:

In order to verify whether we have the correct equation, simply substitute the given points into our derived linear equation:

y-intercept: (0, 8)

y = -x + 8

8 = -(0) + 8

8 = 0 + 8

8 = 8 (True statement).

x-intercept: (8, 0)

y = -x + 8

0 = -(8) + 8

0 = -8 + 8

0 = 0 (True statement).

Final

Therefore, the correct answer is Option B: y = -x + 8

___________________________Keywords:

Slope-intercept form

Linear Equations

Linear Functions

Slope

Y-intercept

X-intercept

_______________________________

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determine the equation of the line that intersects the y-axis at(0,8) and intersects X-axis at (8,0)...