Answer:
slope perp. 1/2
y -2 = 1/2(x - 4)
y - 2 = (1/2)x - 2
y = (1/2)x
Step-by-step explanation:
An equation of the perpendicular line in slope-intercept form is [tex]y=\frac{1}{2}x[/tex].
The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.
For the given situation,
The line is [tex]y = -2x+3[/tex] ------- (1)
The general form of equation of line in slope intercept form is
[tex]y=mx+c[/tex] -------- (2)
On comparing equation 1 and 2, we get the slope as
[tex]m_{1} =-2[/tex]
When two lines are perpendicular to each other, then their slopes are negative reciprocal of the given line.
So, the slope of the perpendicular line is
⇒ [tex]m_{2} =-\frac{1}{m_{1} }[/tex]
⇒ [tex]m_{2} =-\frac{1}{-2}[/tex]
⇒ [tex]m_{2} =\frac{1}{2}[/tex]
The perpendicular line has the slope m₂ is 1/2 and passing through the point (4,2),
⇒ [tex]2=\frac{1}{2} (4)+c[/tex]
⇒ [tex]2=2+c[/tex]
⇒ [tex]c=2-2[/tex]
⇒ [tex]c=0[/tex]
Thus an equation of the perpendicular line in slope-intercept form is
⇒ [tex]y=\frac{1}{2}x+0[/tex]
⇒ [tex]y=\frac{1}{2}x[/tex]
Hence we can conclude that an equation of the perpendicular line in slope-intercept form is [tex]y=\frac{1}{2}x[/tex].
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