Question

How do you write an equation in slope intercept form given $\left( { - 4,3} \right)$ and $m = - 3$?

Answer 1

In this question we have to find the equation of line in slope intercept form, where slope and a point is given, we know that slope intercept form is given by $y = mx + b$ , where $m$ is the slope of the line and $b$ is the $y$-intercept of the line, now by substituting the given point in the slope intercept form we will get the $y$-intercept of the line, then by using $y$-intercept and the given slope we will get the required equation in slope intercept form.

Complete step by step solution:
Given point is $\left( { - 4,3} \right)$and slope is $m = - 3$,
We know that slope intercept form is given by $y = mx + b$ , where $m$ is the slope of the line and $b$ is the $y$-intercept of the line,
As the given point passes through the equation, we can substitute the point in the slope intercept form, we get
So, here $y = 3$, $m = - 3$ and $x = - 4$, by substituting the values in the slope intercept form we get,
$\Rightarrow 3 = \left( { - 3} \right)\left( { - 4} \right) + b$,
Now simplifying we get,
$\Rightarrow 3 = 12 + b$,
Now subtracting 12 on both sides we get,
$\Rightarrow 3 - 12 = 12 + b - 12$,
Now simplifying we get,
$\Rightarrow b = - 9$,
So, here we got $y$-intercept of the line $b = - 9$ and slope of the line $m = - 3$, now substituting the values in the slope intercept form i.e., $y = mx + b$ we get,
$\Rightarrow y = \left( { - 3} \right)x - 9$,
Now simplifying we get
$\Rightarrow y = - 3x - 9$,
So, the slope intercept equation is $y = - 3x - 9$.

$\therefore$The required equation in slope intercept form will be equal to $y = - 3x - 9$.

Note: Remember that if the slope of a line is equal to zero then it is parallel to x-axis and if the slope tends to infinity then it is perpendicular to x-axis. Also, we can remember that if the x-coordinates of the two points through which the line passes are same it must be perpendicular to the x-axis and y-coordinates of the two points through which the line passes are same it must be parallel to the x-axis.