Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Writing the equation of the line through two given points(-4,-1) (2,-5). y=mx-b form

Sagot :

So we are given two points and we have to use them to construct the equation of a line in slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept. With two given points we can construct two equations for m and b. For example, if we know that the line passes through two generic points (A,B) and (C,D) we have the following equations that are the result of taking (x,y)=(A,B) and (x,y)=(C,D):

[tex]\begin{gathered} B=A\cdot m+b \\ D=C\cdot m+b \end{gathered}[/tex]

The points we have are (-4,-1) and (2,-5). Then we have A=-4, B=-1, C=2 and D=-5 and the two equations for m and b are:

[tex]\begin{gathered} -1=-4m+b \\ -5=2m+b \end{gathered}[/tex]

We can take the first equation and add 4m to both sides:

[tex]\begin{gathered} -1+4m=-4m+b+4m \\ b=4m-1 \end{gathered}[/tex]

Then we substitute b with this expression in the second equation:

[tex]\begin{gathered} -5=2m+b \\ -5=2m+4m-1 \\ -5=6m-1 \end{gathered}[/tex]

And we add 1 to both sides:

[tex]\begin{gathered} -5+1=6m-1+1 \\ -4=6m \end{gathered}[/tex]

And we divide both sides by 6:

[tex]\begin{gathered} -\frac{4}{6}=\frac{6m}{6} \\ m=-\frac{4}{6}=-\frac{2}{3} \end{gathered}[/tex]

Then we use this value in the expression for b:

[tex]\begin{gathered} b=4m-1=4\cdot(-\frac{2}{3})-1 \\ b=-\frac{8}{3}-1 \\ b=-\frac{11}{3} \end{gathered}[/tex]

Thent the equation we are looking for and answer to this question is:

[tex]y=-\frac{2}{3}x-\frac{11}{3}[/tex]

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.