Question

Determine the linear function whose graph is a line that contains the points (7, 4) and (1, -3)

• A. $\frac{7}{6}x+\frac{25}{6}$
• B. $-\frac{7}{6}x+\frac{25}{6}$
• C. $\frac{1}{6}x+\frac{25}{6}$
• D. $\frac{7}{6}x-\frac{25}{6}$

Answer 1

Answer: (D)

$\frac{7}{6}x-\frac{25}{6}$

Using $f\left(x\right)$=$ax+b$ to represent the linear function, we know that for this problem
$f\left(7\right)=7a+b=4$ and $f\left(1\right)=a+b=-3$. Thus, we have the following system to solve
$7a+b=4$ ......... (1)
$a+b=-3$ ......... (2)
Eq. (2) can be replaced with an eq. formed by multiplying eq. (1) by -1 and adding that result to eq. (2)
$7a+b=4$ ......... (3)
$-6a=-7$ ............ (4)
From eq (4) we can find that a $=$ 7/6. Then we can substitute 7/6 for a in eq. (2)
$a+b=-3$
$\frac{7}{6}+b=-3;b=-3-\frac{7}{6}\Rightarrow b=-\frac{25}{6}$
The linear function is $f\left(x\right)=\frac{7}{6}x-\frac{25}{6}$