Question

The graph of the line $y=mx+b$ is given by some random points. What is the slope and 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 A $m=-2,b=3$

Given Line: $y=mx+b$,
where $m=$ slope, $b=$ intercept.

$\text{Slope}=\frac{\text{rate of change of y}}{\text{rate of change of x}}=\frac{\text{rise/fall}}{\text{run}}$

How to check graph is falling or rising:

• When $x$ is increasing and $y$ is also increasing then graph is rising.
• When $x$ is increasing and $y$ is decreasing then graph is falling.

From the above graph,
$x=-1,y=5$
$x=0,y=3$
$x=1,y=1$
$x=2,y=-1$
Here, $x$ value is increasing and $y$ value is decreasing continuously. So, this graph is falling.

Find $\frac{rise/fall}{run}$:
Here, line intersect $y$ axis at $(0,3)$. So, $y$ value is $3$.
Since, graph is falling, hence $y$ value will be negative.
So, fall $=-3$

Here, graph intersect x axis at $(1.5,0)$. $x$ value will be $1.5$.
Hence, run $=1.5-0=1.5$

So, slope $m=\frac{\text{fall}}{\text{run}}$
$=-\frac{3}{1.5}$
$=-2$

How to find intercept from graph:
$y$ is the intercept of the given line.
Here, graph intersect $y$ axis at $(0,3)$. So, $y$ value is $3$. Hence intercept is $3$.