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Sagot :
The point-slope form of the equation for the line with a slope of [tex]\frac{6}{19}[/tex] that passes through the point[tex](-1,\frac{7}{5} )[/tex] is [tex]6x-19y=-\frac{163}{5}[/tex]
As per the question statement, we are supposed to find the point-slope form of the equation for the line with a slope of [tex]\frac{6}{19}[/tex] that passes through the point[tex](-1,\frac{7}{5} )[/tex] .
Before solving the question, we need to know about the point - slope form of the line i.e., [tex]y-y_{1} =m(x-x_{1} )[/tex]
where m = slope = [tex]\frac{6}{19}[/tex]
[tex]x_{1} =-1[/tex] and [tex]y_{1} = \frac{7}{5}[/tex]
Now substituting values, we get
[tex]y-\frac{7}{5} =\frac{6}{19} (x-[-1])[/tex]
[tex]y-\frac{7}{5} = \frac{6}{19} (x+1)[/tex]
[tex]19y - \frac{133}{5} = 6x+6[/tex]
Rearranging,
[tex]6x-19y+6+\frac{133}{5} =0[/tex]
[tex]6x-19y+\frac{163}{5} =0[/tex]
[tex]6x-19y=-\frac{163}{5}[/tex]
Hence our required equation is [tex]6x-19y=-\frac{163}{5}[/tex]
- Point slope form of equation: The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
To learn more about equations of line, click the link given below:
https://brainly.com/question/14200719
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