Question

Which one of the following equations correctly represents the following graph?

• A. $y=\frac{1}{2}x+5$
• B. $y=-\frac{1}{2}x+5$
• C. $y=-\frac{1}{2}x-5$
  
• D. $y=-\frac{1}{2}x-5$

Answer 1

The correct option is C $y=-\frac{1}{2}x-5$



From the graph, we can observe that
y-intercept value is -5.
$\Rightarrow$ Value of b = -5

Let us consider two points from the graph, say (0,-5) and (-10,0).

We know, Slope = $\frac{\text{Change in y-axis}}{\text{Change in x-axis}}$

∴ By putting the values, we get,
Slope ($m$) $=\frac{0-(-5)}{-10-0}$
$=\frac{5}{-10}$
$=-\frac{1}{2}$

Equation of a line with y-intercept value of $b$ is $y=mx+b$.

$\therefore$ Equation of the graph is $y=-\frac{1}{2}x-5$.