Question

The slope of the given line of best fit is $-50.$ It passes through the point $(1.5,37.5).$ Find the equation of the line and the value of $u$ for $v=\mathrm{0.75.}$

• A. Equation of the line: $u-37.5=50(v-1.5)$
• B. Equation of the line: $u-37.5=-50(v-1.5)$
• C. For $v=0.75,u=7.5$
• D. For $v=0.75,u=75$

Answer 1

Answer: (B), (D)

For $v=0.75,u=75$

Given, slope of the line, $m=-50$

Equation of line in point form is
$y-y_1=m(x-x_1)$
Replacing the variable $y$ with $u$ and $x$ with $v,$ as per the given plot
$u-u_1=m(v-v_1)$
It passes through the point $(v_1,u_1)=(1.5,37.5)$

$\therefore$ Equation of the line is
$u-37.5=-50(v-1.5)$

For $v=0.75,$
$u-37.5=-50(0.75-1.5)$
$\Rightarrow u-37.5=-50\times (-0.75)$
$\Rightarrow u-37.5=37.5$
$\Rightarrow u=37.5+37.5=75$

Options (b) and (d) are correct.