Respuesta :
The required equation of line is: [tex](y - 4)= \frac{3}{5}(x+6)[/tex]
What is the equation of a line to the curve?
- A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c.
- It is a first-order equation with the variables x and y.
- The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.
Given:
- Equation of line: 5x + 3y = 5
- New line passes through the point (-6,4)
- New line perpendicular to given line.
To find: Equation of new line
Finding:
- Given equation of line: 3y = 5 - 5x
=> y = [tex]\frac{5}{3} (1-x) = \frac{-5}{3}(x-1)[/tex]
- On comparison with a standard equation of line: [tex](y-y_0) = m(x-x_0)[/tex], where,
- m = slope of the line
- [tex](x_0,y_0)[/tex] = coordinates of point through which the line passes.
We get: m = -5/3 and [tex](x_0,y_0)[/tex] = (1,0) for the given line.
- Now, since the given line is perpendicular to the new line,
Slope of the new line = m' = [tex]\frac{-1}{m} = \frac{3}{5}[/tex]
Hence, On substituting the values for [tex](x_0,y_0)[/tex] and m', we get the equation of the new line as:
[tex](y - 4)= \frac{3}{5}(x+6)[/tex]
To learn more about equation of a line to a curve, refer to the link: https://brainly.com/question/13763238
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