if f(x) is a linear function, what is the value of n?\n| x | f(x) |\n| -4 | -25 |\n| -1 | -10 |\n| n | 20…
if f(x) is a linear function, what is the value of n?\n| x | f(x) |\n| -4 | -25 |\n| -1 | -10 |\n| n | 20 |\n2\n4\n5\n9
Answer
Explanation:
Step1: Find the slope of the linear function
The slope $m$ of a linear - function is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(-4,-25)$ and $(-1,-10)$: $m=\frac{-10-(-25)}{-1 - (-4)}=\frac{-10 + 25}{-1+4}=\frac{15}{3}=5$.
Step2: Use the point - slope form to find the equation of the line
The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-1,-10)$ and $m = 5$, we have $y-(-10)=5(x - (-1))$, which simplifies to $y + 10=5(x + 1)$ and further to $y=5x+5 - 10=5x - 5$.
Step3: Find the value of $n$
Since $y = f(x)=20$, we substitute $y = 20$ into the equation $y = 5x-5$. $20=5x-5$. Add 5 to both sides: $20 + 5=5x$, so $25 = 5x$. Divide both sides by 5: $x=\frac{25}{5}=5$. So $n = 5$.
Answer:
5