The equation of line is:
[tex]y = \frac{-3}{2}x+1[/tex]
Further explanation:
The standard form of equation in point-slope form is:
[tex]y = mx+b[/tex]
Given equation is:
3x+2y=10
We have to convert it into point slope form, for which we have to isolate y on one side of equation
[tex]3x+2y = 10\\2y = -3x +10\\y = \frac{-3}{2}x + \frac{10}{2}\\y = \frac{-3}{2}x + 5[/tex]
Comparing with standard form:
m = -3/2
As the new line is parallel to given line, their slopes will be equal
So,
[tex]y = \frac{-3}{2}x+b[/tex]
To find the value of b, putting the given point (4,-5) in equation
[tex]-5 = \frac{-3}{2}(4)+b\\-5 = -6+b\\b = -5+6 \\b = 1\\So\ the\ equation\ is:\\y = \frac{-3}{2}x+1[/tex]
Keywords: Point-slope form, equation of line
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