Equation of line is the equation which tell us about the slope of the line and the intercept of the line at y-axis in the graph. The equation of a line which through the point (2,-4) and (6,10) is,
\(y=\dfrac{7}{2} x-11\)
Given-
The points through which the line passes are (2,-4) and (6,10).
What is the equation of line?
Equation of line is the equation which tell us about the slope of the line and the intercept of the line at y-axis in the graph
The equation of a line with a known slope m can also be written as,
\(y=mx+b\)
Here, m is the slope of the line and b is the y intercept on the graph of the line.The formula to find the slope of the line can be given as,
\(m=\dfrac{y_2-y_1}{x_2-x_1}\)
\(m=\dfrac{10-(-4)}{6-2}\)
\(m=\dfrac{14}{4}\)
\(m=\dfrac{7}{2}\)
Now the equation of line,
\((y-y_1)=m(x-x_1)\)
\([y-(-4)]=\dfrac{7}{2} (x-2)\)
\(y+4=\dfrac{7}{2} x-7\)
\(y=\dfrac{7}{2} x-7-4\)
\(y=\dfrac{7}{2} x-11\)
Hence the equation of a line which through the point (2,-4) and (6,10) is,
\(y=\dfrac{7}{2} x-11\)
Learn more about the equation of line here;
https://brainly.com/question/2564656
