Respuesta :
a.) 4x-8y=8 move the x over to the other side
-8y=-4x+8 divide everything by -8.
y=1/2x-1
b.) In slope-intercept form, it has a form of y=mx+b where m is the slope, and b is the y-intercept. So, the slope is 1/2, and the y-intercept is (0,-1).
c.) First, if you see the word perpendicular to this line, you will need to negative reciprocate the slope. Which means you flip the fraction and add a negative sign (or remove if there is one existing). The form of point-slope is y-y1=m(x-x1) and since the slope is 1/2 in the original, the perpendicular one would be y-2=-2(x-1) if you need slope intercept form it can simplify to y-2=-2x+2, then add two to both sides to make it y=-2x+4.
-8y=-4x+8 divide everything by -8.
y=1/2x-1
b.) In slope-intercept form, it has a form of y=mx+b where m is the slope, and b is the y-intercept. So, the slope is 1/2, and the y-intercept is (0,-1).
c.) First, if you see the word perpendicular to this line, you will need to negative reciprocate the slope. Which means you flip the fraction and add a negative sign (or remove if there is one existing). The form of point-slope is y-y1=m(x-x1) and since the slope is 1/2 in the original, the perpendicular one would be y-2=-2(x-1) if you need slope intercept form it can simplify to y-2=-2x+2, then add two to both sides to make it y=-2x+4.
[tex]m=\frac{1}{2}[/tex]For the given equation 4x - 8y = 8,
a. The slope-intercept form for the given equation is y = [tex]\frac{1}{2} x-1[/tex]
b. The slope of the line is [tex]m=\frac{1}{2}[/tex] and the y-intercept of the line is c = -1
c. The equation of the line that is perpendicular to the given line 4x - 8y = 8 and passes through the point (1,2) is (y-2)= -2(x-1) or y= -2x+4.
How to represent a line slope-intercept form?
The standard slope-intercept form of a line is y=mx+c. Where m is the slope and c is the y-intercept.
For a line given in the form of ax+by+c=0,
The slope m is calculated as -a/b and the y-intercept is calculated as -c/b.
How to find a perpendicular line for a given line passing through a point?
The given line has slope m=-a/b and y-intercept c. So, for the perpendicular line, the slope is calculated as -1/m (the negative reciprocal of the slope of the given line)
The equation of the line passing through a point (x1, y1) and with a slope -1/m is
(y-y1) = -1/m (x-x1) (point-slope form)
Calculation:
Given line is 4x - 8y = 8
we can write it in the form of ax+by+c=0
⇒ 4x - 8y -8 =0
⇒ 4 (x-2y-2) =0
⇒ x-2y-2=0
On comparing with ax+by+c=0, we have a=1, b=-2 and c=-2
a). Transforming the equation into the slope-intercept form:
For the line Slope m = -a/b
⇒ [tex]m=-\frac{1}{-2} =\frac{1}{2}[/tex]
The y-intercept c = -c/b
⇒ [tex]c=-\frac{-2}{-2}=-1[/tex]
Then, the slope-intercept form of the given line is [tex]y=\frac{1}{2}x-1[/tex].
b). The slope of the given line is [tex]m=\frac{1}{2}[/tex] and the y-intercept of the line is c = -1
c). Finding the perpendicular line:
The given line is x-2y-2=0
It has a slope [tex]m=\frac{1}{2}[/tex] and the y-intercept is c = -1
Then, the slope for the perpendicular line is calculated as follows:
The slope of the perpendicular line m = [tex]-\frac{1}{m} = -2[/tex]
Then the line that is perpendicular to the given line x-2y-2=0 and passes through the point (1,2) is
(y-y1) = m(x-x1) (point-slope form)
(y-2) = -2(x-1)
or
y-2 = -2x+2
⇒ y = -2x+4
Therefore, the perpendicular line is (y-2) = -2(x-1) or y = -2x+4.
Learn more about the slope-intercept form of a line here:
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