An equation of the line that passes through the given point and is parallel to the given line is: [tex]y = -2x+9[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]y = -2x+7[/tex]
Let m1 be the slope of given line.
As the equation of line is in slope-intercept form, the coefficient of x is the slope of the line
So
m1 = -2
Let m2 be the slope of 2nd line
m2 = -2
as slopes of parallel lines are equal
The slope-intercept form is:
[tex]y =m_2x+b[/tex]
Putting the value of m2
[tex]y=-2x+b[/tex]
Putting (4,1) in the equation
[tex]1 = -2(4)+b\\1= -8+b\\b =1+8\\b=9[/tex]
Putting the values of m and b we et
[tex]y = -2x+9[/tex]
An equation of the line that passes through the given point and is parallel to the given line is: [tex]y = -2x+9[/tex]
Keywords: Equation of line, slope
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