Question

Find the slope of the line through the points (4, -1) and (1, -4) and then graph it. Slope=

Answer 1

Given:

Line pass through the point ( 4, -1 ) and ( 1, -4 )

Find-:

The slope of the line and graph of the line.

Explanation-:

The slope of the line is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where,

$\begin{gathered} m=\text{ Slope} \\ \\ (x_1,y_1)=\text{ First point} \\ \\ (x_2,y_2)=\text{ Second point} \end{gathered}$

Given point is:

$\begin{gathered} (x_1,y_1)=(4,-1) \\ \\ (x_2,y_2)=(1,-4) \end{gathered}$

The slope of the line is:

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{-4-(-1)}{1-4} \\ \\ m=\frac{-4+1}{1-4} \\ \\ m=\frac{-3}{-3} \\ \\ m=1 \end{gathered}$

The slope of the line is 1.

For a graph of lines,

Equation of line is:

$y=mx+c$

Where,

$\begin{gathered} m=\text{ Slope} \\ \\ c=Y-\text{ intercept} \end{gathered}$

So, the equation become

$\begin{gathered} y=mx+c \\ \\ y=1x+c \\ \\ y=x+c \end{gathered}$

For value of "c" is:

Point = ( 4, -1)

$\begin{gathered} y=x+c \\ \\ (x,y)=(4,-1) \\ \\ y=x+c \\ \\ -1=4+c \\ \\ c=-1-4 \\ \\ c=-5 \end{gathered}$

So, the equation

$\begin{gathered} y=mx+c \\ \\ y=x-5 \end{gathered}$

So, the graph of line is: