Respuesta :
The graph of the line y = -x + 8 is as shown below.
What is the slope-point form of equation of the line?
"The equation of the line having slope m and passing through (p, q) is,
(y - q) = m(x - p)."
What is the graph of a function?
"It is a set of all points of the form (x, f(x))"
For given example,
We have been given the slope of the line.
m = -1
And the line passes through the point (3,5)
Let (p, q) = (3, 5)
Using the slope-point form the equation of the line would be,
⇒ (y - q) = m(x - p)
⇒ (y - 5) = (-1) × (x - 3)
⇒ y - 5 = -x + 3
⇒ y = -x + 8
So, the equation of the line is y = -x + 8
Now, to plot the graph of the line, first we find the coordinates of the points.
For x = 0,
⇒ y = -(0) + 8
⇒ y = 8
For x = 1
⇒ y = -1 + 8
⇒ y = 7
For x = -2
⇒ y = -(-2) + 8
⇒ y = 2 + 8
⇒ y = 10
So, the coordinates of the points are (0, 8), (1, 7), (-2, 10)
Now, we plot these points on the coordinate plane and draw a line passing through these points.
The graph of the line y = -x + 8 is as shown below.
Learn more about the slope-point form of the line here:
https://brainly.com/question/24436844
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