Respuesta :
Answer:
The value of n is 5.
Step-by-step explanation:
We have been given that f(x) is a linear function and we are asked to find the value of n from the provided table.
x f(x)
-4 -25
-1 -10
n 20
First of all we will find the slope of the given using our given points (-4,-25) and (-1,-10) in slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Upon substituting coordinates of our given points we will get,
[tex]m=\frac{-10--25}{-1--4}[/tex]
[tex]m=\frac{-10+25}{-1+4}[/tex]
[tex]m=\frac{15}{3}[/tex]
[tex]m=5[/tex]
Since we know that the equation of a line in slope-intercept form is: [tex]y=mx+b[/tex], where, m= Slope and b= y-intercept.
Upon substituting m = 5 in slope-intercept form of equation we will get,
[tex]y=5x+b[/tex]
Now let us find y-intercept by substituting coordinates of one point in our given line.
[tex]-10=5(-1)+b[/tex]
[tex]-10=-5+b[/tex]
[tex]-10+5=-5+5+b[/tex]
[tex]-5=b[/tex]
So the equation of given line will be,
[tex]y=5x-5[/tex]
Now let us find value of n by substituting x = n and y = 20 in our equation.
[tex]20=5*n-5[/tex]
[tex]20+5=5*n-5+5[/tex]
[tex]25=5*n[/tex]
[tex]\frac{25}{5}=\frac{5*n}{5}[/tex]
[tex]5=n[/tex]
Therefore, the value of n is 5.
