Two point-slope equations for the line passing through the points
(6, 5) and (3, 1) are,
- [tex]y-5=\frac{4}{3}(x-6)[/tex]
- [tex]y-1=\frac{4}{3}(x-3)[/tex]
Point-slope equations
- Point-slope exists in the general form y-y₁=m(x-x₁) for linear equations. It underlines the slope of the line and a point on the line (that exists not the y-intercept).
- The slope formula exists utilized to calculate the inclination or steepness of a line. It discovers application in choosing the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis. The slope of a line exists defined as the change in the "y" coordinate concerning the change in the "x" coordinate of that line.
Here, the line passes through the points (6,5) and (3,1).
Let,
[tex]$(6,5)=\left(x_{1}, y_{1}\right)$[/tex]
[tex]$(3,1)=\left(x_{2}, y_{2}\right)$[/tex]
Substitute
Slope(m) = [tex]\frac{1-5}{3-6}=\frac{-4}{-3}[/tex]
Slope(m) =[tex]\frac{4}{3}[/tex]
Point-slope equations of the line passing through [tex]$(6,5 \6})$[/tex] and [tex](3}, 1)$[/tex]
Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(6,5)$[/tex]into [tex]$y-b=m(x-a)$[/tex]
[tex]y-5=\frac{4}{3}(x-6)[/tex] (point-slope equation)
Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(3,1)$[/tex] into [tex]$y-b=m(x-a)$[/tex]
[tex]$y-1=\frac{4}{3}(x-3)$[/tex] (point-slope equation)
To learn more about Point-slope equations refer to:
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