The equation of a line that is parallel to the line whose equation is 4x+3y=7 and also passes through the point (-6,2) is: [tex]y = -\frac{4}{3}x-6[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]4x+3y = 17[/tex]
We have to convert the given line in slope-intercept form to find the slope of the line
So, Subtracting 4x from both sides
[tex]4x+3y-4x = -4x+7\\3y = -4x+7[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3} = \frac{-4x+7}{3}\\y = \frac{-4x}{3} + \frac{7}{3}\\y = -\frac{4}{3}x+\frac{7}{3}[/tex]
The co-efficient of x is the slope of the line.
Let m1 be the slope of given line
[tex]m_1 = -\frac{4}{3}[/tex]
As the line is parallel to given line, slope of both lines will be equal
Let m be the slope of line parallel to given line
m = [tex]-\frac{4}{3}[/tex]
The slope-intercept form is:
[tex]y=mx+b[/tex]
Putting the value of slope
[tex]y = -\frac{4}{3}x+b[/tex]
Putting the point (-6,2) in the equation
[tex]2 = -\frac{4}{3} (-6) +b\\2 = 4*2 + b\\2 = 8+b\\b = 2-8\\b = -6[/tex]
Putting the value of b
[tex]y = -\frac{4}{3}x-6[/tex]
Hence,
The equation of a line that is parallel to the line whose equation is 4x+3y=7 and also passes through the point (-6,2) is: [tex]y = -\frac{4}{3}x-6[/tex]
Keywords: Equation of line, slope
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