Question

How do you write an equation of the line given $\left( {m = - 3} \right)$ and $\left( {b = 5} \right)$?

Answer 1

You are given a slope and intercept of a line and we have to find its equation for this will use the slope intercept equation to form a line i.e.
$Y=mX+c$
Here m is the slope and intercept of a line and c is the y-intercept of line. We will substitute the values in the equation and form the equation of the straight line.

Complete step-by-step answer:
Step1: We are given a slope $\left( {m = - 3} \right)$ and $\left( {b = 5} \right)$ we have to find the equation of the line using the slope-intercept form of a line i.e.
$Y=mX+c$
Here, $\left( {m = - 3} \right)$ and $c = - 5$.
On substituting the values in the formula we will get:
$\Rightarrow y = \left( { - 3} \right).x + b$
Step2: Now we will replace the known value of b in the slope y- intercept form of the equation we will get:
$\Rightarrow y = \left( { - 3} \right).x + 5$
On removing the parenthesis we get the equation:
$\Rightarrow y = - 3x + 5$

Hence, the equation of line is $y = - 3x + 5$

Note:
In solving these types of questions students get confused which formula to apply. Because there are many equation forms of line. But when slope and intercept is given only apply one form that is slope intercept form. Sometimes slope is not given so it can be found using the formula of slope. The formula of slope is $m= \dfrac{y_2-y_1}{x_2-x_1}$. Here $y_2$ & $y_1$ are y coordinates and $x_1$ & $x_2$ are x coordinates. Many times intercept is given like the line passes through a point (0, 3). Here 3 is the y intercept. Students should also keep in mind the signs because many times they forget to put the signs or sometimes they do the wrong cancellation of signs.