The equation that represents the graphed function is the option: A (Y=-2x+3). This is obtained by using the slope-intercept form of the given graphed function.
What is the slope-intercept form of a line?
The slope-intercept form of a line is given by the equation Y=mx+c.
Where m is the slope and c is the y-intercept.
How to find the slope of a line with two points?
The slope of a line is the ratio of the difference of y-coordinates to the difference of x-coordinates of the given two points. I.e.,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using this the equation of the line can be written as
[tex]y-y_1=m(x-x_1)[/tex]
Finding the equation for the given graphed function:
Given that,
The line passes through two pints (0,3) and (1,1) i.e., x1=0, y1=3, x2=1 and y2=1.
So, the slope m is calculated as
[tex]m=\frac{1-3}{1-0}[/tex]
⇒ m = -2
Then the equation of the line is calculated as follows:
[tex]y-y_1=m(x-x_1)\\[/tex]
⇒y - 3= (-2)(x-0)
⇒y - 3= -2x
⇒ y = -2x+3
Thus, this is in the slope-intercept form as Y=mx+c
Where, m=-2 and c=3
Therefore, option A: Y=-2x+3 represents the equation of the given graphed function.
Learn more about slope-intercept form here:
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