Answer:
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:
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
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:
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}\:=\:\frac{0-8}{8-0}\:=\:\frac{-8}{8}\:=-1}[/tex]
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 Answer:
Therefore, the correct answer is Option B: y = -x + 8
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Keywords:
Slope-intercept form
Linear Equations
Linear Functions
Slope
Y-intercept
X-intercept
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Learn more about linear equations here:
https://brainly.com/question/18176080
