Question

How do you write an equation in slope intercept form given $\left( 1,-3 \right)$ and $\left( -2,-4 \right)$?

Answer 1

In this problem we have to find the equation is slope intercept form. We know that the equation of slope intercept form is $y=mx+c$, where m is the slope and c is the y-intercept. Here we are given two points, with which we can find the slope using slope formula of two points and we can substitute any one of the points in the slope intercept form to find the y-intercept, we can then substitute the slope, m and y-intercept, c in the formula to find the equation.

Complete step by step answer:
We can now find the equation by using slope intercept form.
We know that the slope intercept form of the line is,
$y=mx+c$ ……. (1)
Where, m is the slope and c is the y-intercept.
We have two points, $\left( {{x}_{1}},{{y}_{1}} \right)$=$\left( 1,-3 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$=$\left( -2,-4 \right)$.
Slope, m = $\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\dfrac{-4+3}{-2-1}=\dfrac{-1}{-3}=\dfrac{1}{3}$ .
The slope value, m is $\dfrac{1}{3}$
We can substitute the slope value in equation (1), we get
$y=2x+c$
We can now substitute the x and y value from any of the two points to get the y-intercept.
We can take the point $\left( 1,-3 \right)$

& \Rightarrow -3=\dfrac{1}{3}\left( 1 \right)+c \\\ & \Rightarrow c=-3-\dfrac{1}{3}=-\dfrac{10}{3} \\\ \end{aligned}$$ The y-intercept is $$-\dfrac{10}{3}$$ and the slope is $$\dfrac{1}{3}$$. We can now substitute the above values in (1), we get Therefore, the required equation is $$y=\dfrac{1}{3}x-\dfrac{10}{3}$$.  **Note:** Students make mistakes while finding the value of slope using two points, for which we have a formula $$\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$$ we can substitute the given two points in this formula to find the value of m. we can substitute any of the given point after substituting the slope value in the formula to find the y-intercept.