Discover a world of knowledge and get your questions answered at IDNLearn.com. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.
Sagot :
ANSWER
[tex]2y+x+16=0[/tex]EXPLANATION
We want to find the equation of the line in general form i.e.:
[tex]Ax+By+C=0[/tex]where A, B, C are constants
To do this, we have to first find the slope of the line using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are the two points the line passes through.
We have that the two points are (4, -1) and (-2, -7)
Therefore, the slope of the line is:
[tex]\begin{gathered} m=\frac{-7-(-10)}{-2-4} \\ m=\frac{-7+10}{-2-4} \\ m=\frac{3}{-6} \\ m=-\frac{1}{2} \end{gathered}[/tex]Now, we find the equation of the line in point-slope form by using the formula:
[tex]y-y_1=m(x-x_1)[/tex]Therefore, we have:
[tex]\begin{gathered} y-(-10)=-\frac{1}{2}(x-4) \\ y+10=-\frac{1}{2}x+2 \end{gathered}[/tex]To express it in the general form, first, eliminate the fraction by multiplying both sides of the equation by 2:
[tex]2y+20=-x+4[/tex]Now, take all the terms to the left side of the equation:
[tex]\begin{gathered} 2y+x+20-4=0 \\ 2y+x+16=0 \end{gathered}[/tex]That is the equation of the line in the general form.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.
