Question

The line in the given graph can be plotted using the equation $y=mx+b$. Which among the following options represents the slope and the intercept of the line?

• A. $m=2,b=-3$
• B. $m=-2,b=3$
• C. $m=-2,b=-3$
• D. $m=2,b=3$

Answer 1

The correct option is B $m=-2,b=3$

Equation of the line: $y=mx+b$
Where $m=$ slope, $b=$ intercept.
The $x$ and $y$ coordinates of the points on the line are as follows:
$\begin{array}{cccccc}x& -1& 0& 1& 2& 3\\ y& 5& 3& 1& -1& -3\end{array}$
Note:
The graph is said to be rising if $y$ increases when $x$ increases.
The graph is said to be falling if $y$ decreases when $x$ increases.
Here, the value of $y$ decreases as the value of $x$ increases. So, this graph is said to be falling.
Slope $=\frac{\text{rate of change of}y}{\text{rate of change of}x}=\frac{\text{rise or fall}}{\text{run}}=\frac{3-5}{0-(-1)}=\frac{-2}{1}=-2$
The $y$-coordinate at which the line intersects the $y$-axis is called the intercept of the line.
Here, the graph intersects the $y$-axis at $(0,3).$ So, the value of the $y$-coordinate is $3.$ Hence, the intercept is $3.$