The line parallel to 4 x + y = 3 and passing through (3 ; 2) has equation
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Easiest way:
since the lines are parallel, they would differ only in the constant
so the equation is 4x + y = c
plug in the given point to find c and you are done
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To find the equation of a line parallel to another line, we need to have the same slope. The given line has the equation 4x + y = 3.
To get the slope of the given line, we need to rearrange the equation into slope-intercept form (y = mx + b), where m is the slope.
Let's rearrange 4x + y = 3:
Subtract 4x from both sides:
y = -4x + 3
From this equation, we can see that the slope (m) of the given line is -4.
Now, we have the slope of the given line and a point (3, 2) that the new line needs to pass through.
To find the equation of the line parallel to the given line and passing through (3, 2), we can use the point-slope form of a line:
y - y1 = m(x - x1)
Where (x1, y1) is the point (3, 2), and m is the slope of the given line (-4).
Let's substitute the values into the equation:
y - 2 = -4(x - 3)
Simplify:
y - 2 = -4x + 12
Now, let's put the equation into standard form:
4x + y = 12 + 2
4x + y = 14
Therefore, the equation of the line parallel to 4x + y = 3 and passing through (3, 2) is 4x + y = 14.