The equation of line that passes through the point(5,-3) and is parallel to the line 4x-5y=45 is: [tex]y = \frac{4}{5}x-7[/tex]
Step-by-step explanation:
Given equation is:
[tex]4x-5y = 45[/tex]
First of all we have to convert the equation in slope-intercept form
So,
[tex]4x - 45 = 5y\\5y = 4x-45\\\frac{5y}{5} = \frac{4x-45}{5}\\y = \frac{4x}{5} -\frac{45}{5}\\y = \frac{4}{5}x - 9[/tex]
Let m1 be the slope of given line and m2 be the slope of required line
The coefficient of x is the slope of the line, so
m1 = 4/5
As the required line is parallel to given line, both will have equal slopes
m2 = 4/5
Slope-intercept form is:
[tex]y = m_2x+b[/tex]
Putting the value of m2
[tex]y = \frac{4}{5}x +b[/tex]
Putting the point (5,-3) in the equation
[tex]-3 = \frac{4}{5} (5) +b\\-3 = 4+b\\b = -3-4\\b = -7[/tex]
Putting the value of b
[tex]y = \frac{4}{5}x-7[/tex]
Hence,
The equation of line that passes through the point(5,-3) and is parallel to the line 4x-5y=45 is: [tex]y = \frac{4}{5}x-7[/tex]
Keywords: Slope, equation of line
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