Question

How do you write the equation of the line in slope intercept form given point $\left( 4,-3 \right)$ and has slope $m=1$ ?

Answer 1

In problems like this it is necessary to know the slope and coordinates of a point lying on the straight line to get the equation of it. We can write the equation in its slope intercept form by using the values of the slope and coordinates of the point lying on it. For that we take the general equation of a straight line and put the given values in that equation to get the equation of the straight line.

Complete step-by-step solution:
To get the equation of a straight line in the slope intercept form it is necessary to know the values of the slope and the coordinates of a point lying on it. In this question we are given the value of the slope of the straight line as $1$ and the line passes through the point $\left( 4,-3 \right)$ .
Now, we take the general equation of the straight line in the slope intercept form as
$y=mx+c$
Here, $m$ is the slope and $c$ is the $y$ -intercept of the straight line
Hence, for this problem we can write $m=1$
Now, we substitute the above value of the slope and coordinates of the point $\left( 4,-3 \right)$ in the general equation of the straight line as shown below
$-3=1\times 4+c$
$\Rightarrow c=-7$

Now, we put the value of $m$ and $c$ in the general equation as
$y=x-7$
Therefore, we can conclude that the equation of the straight line is $y=x-7$.

Note: We must do the calculations properly to get the exact correct value of $c$ . Otherwise, the equation will be an inaccurate one. Also, we have to carefully put the proper values of the coordinates of the given point including the signs, as the value of $c$ depends on it.