Question

The given table shows two ordered pairs of a linear equation.
$\begin{array}{ccc}x& 1& 3\\ y& 2& 12\end{array}$
Which of the following represents the linear equation according to the ordered pairs?

• A. $y=5x+3$
• B. $y=3x+5$
• C. $y=3x-5$
• D. $y=5x-3$

Answer 1

The correct option is D $y=5x-3$

The slope-intercept form of a linear equation with two variables is $y=mx+b.$
Where, $m$ is the slope of the line.
$m=\frac{\text{change in}y}{\text{change in}x}=\frac{y_2-y_1}{x_2-x_1}$
Substituting the ordered pairs, we get
$m=\frac{12-2}{3-1}$
$\Rightarrow m=\frac{10}{2}$
$\Rightarrow m=5$
The general equation is $y=mx+b$
By substituting one of the ordered pairs, we get
$\Rightarrow 2=5\left(1\right)+b$
$\Rightarrow 2=5+b$
$\Rightarrow b=2-5$
$\Rightarrow b=-3$
Hence, the correct equation is $y=5x-3$.