The required equation of the line in slope-intercept form that is perpendicular to line y = 2x-1 and passes through the point (1, 3) is 2y + x = 7.
Equation of line in Slope intersept form
The general formula for slope-intercept form is
y = mx + b --(*)
We need to know about perpendicular lines is that they have the negative reciprocal slope of the line they are perpendicular to. This means is that you take the first line's slope, add a negative sign, and switch the numerator and denominator, and that's the slope of the perpendicular line.
In this question, y = 2x-1 is our original line.
Comparing our given line to standard line equation (*), we get
slope of line (m) = 2 and b = -1
we want be negative slope that is -2. Then, switch numerator and denominator we have
-2 is really -2/1, so let's make it -1/2.
The slope of the perpendicular line is -1/2.
Now, we have to make it pass through (1,3).
putting all value in equation of line,
y = (-1/2)x + b
we plug in the x-coordinate = 1 and y-coordinate = 3 we get , 3 = (-1/2) 1 + b
=> 3 +1/2 = b => b = 7/2
Thus the required new line equation is
y = -1/2x + 7/2
or 2y = - x + 7 => x + 2y = 7
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Complete question:
Write an equation for a line perpendicular to y = 2 x − 1 and passing through the point (1,3)
