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On a coordinate plane, a straight line with a negative slope, labeled f of x, crosses the y-axis at (0, 4), and the x-axis at (4, 0). Which is true regarding the graphed function f(x)? f of 0 = 3 f of 5 = negative 1 f of 3 = 2 f of 2 = negative 2

Respuesta :

Answer: 1 f of 3 = 2 f of 2 = negative

Step-by-step explanation:

varshamittal029

The correct option is option 3 i.e. f(5)=-1.

What is the equation of straight line in slope and y-intercept form?

If the slope of the line is m, and y-intercept is c, then the equation of line can be written as y=mx+c.

In function form, it will be y=f(x)=mx+c

So, according to the question,

On the coordinate plane, staright line of negative slope crosses y-axis at the point (0,4) and the x-axis at the point (4,0)

as, line touches y-axis at (0,4) i.e. at that point, x-coordinate=0 and y-coordinate=4

we can say f(0)=4

similarly line touches x-axis at (4,0) i.e. at that point x-coordinate=4 and y-coordinate=0

we can say f(4)=0

so putting these value in function of line

f(0)=4

⇒0.x+c=4

⇒c=4

now function will be=mx+4

f(4)=0

⇒4m+4=0

⇒4m=-4

⇒m=-4/4

⇒m=-1

m is also negative according to question.

the function of line=f(x)=-x+4

checking all the option,

  1. f(0)=-0+4=4 i.e. the option 1 is incorrect.
  2. f(5)=-5+4=-1 i.e. the option 2 is correct.
  3. f(3)=-3+4=1 i.e. the option 3 is incorrect.
  4. f(2)=-2+4=2 i.e. the option 4 is incorrect.

Therefore the correct option is option 3 i.e. f(5)=-1.

Learn more about the equation of line

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