Solveeit Logo
Login

Question

Question: How do you write an equation in standard form given point \(\left( -5,4 \right)\) and slope \(-3\)?...

How do you write an equation in standard form given point (−5,4)\left( -5,4 \right) and slope −3-3?

Explanation

Solution

Here in this question we will use the standard form of equation of line given as (y−y1)=m(x−x1)\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right), where m is the slope of line and (x1,y1)\left( {{x}_{1}},{{y}_{1}} \right) is the point a line passes through. By substituting the values in the formula and simplifying the obtained equation we get the desired answer.

Complete step by step solution:
We have been given the point a line passes through (−5,4)\left( -5,4 \right) and slope −3-3.
We have to write the standard equation of line.
Now, we know that the standard form of a line passes through the point (x1,y1)\left( {{x}_{1}},{{y}_{1}} \right) and has slope m is given as (y−y1)=m(x−x1)\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)
Now, we have x1=−5,y1=4,m=−3{{x}_{1}}=-5,{{y}_{1}}=4,m=-3
Now, substituting the given values in the formula we will get
⇒(y−4)=−3(x−(−5))\Rightarrow \left( y-4 \right)=-3\left( x-\left( -5 \right) \right)
Now, simplifying the above obtained equation we will get
⇒y−4=−3(x+5) ⇒y=−3x−15+4 ⇒y=−3x−11 \begin{aligned} & \Rightarrow y-4=-3\left( x+5 \right) \\\ & \Rightarrow y=-3x-15+4 \\\ & \Rightarrow y=-3x-11 \\\ \end{aligned}
Hence above is the required equation of a line.

Note: The point to be noted is that do not substitute the value of points in place of x and y in the formula, it gives incorrect answer. Also we can find the equation of line by using the slope-intercept form of the line y=mx+cy=mx+c, where m is the slope of line and c is the y-intercept of the line. We can substitute the given points and find the value of y-intercept. Then by substituting the value of slope and y-intercept we get the equation of a line.