Answer:
1. Not possible. The slope of such a line is undefined. Its equation is x=7.
2. y = 3x -2
3. The slope is undefined. (The line is a vertical line.)
Step-by-step explanation:
1. The y-axis is a vertical line. Computing the slope of such a line involves division by zero, an operation that is undefined. Since the line is parallel to the y-axis, there is no y-intercept.
In slope-intercept form, the equation would be useless:
... y = (undefined)x + (no such value)
If your point is supposed to be (7, 8)*, the more useful equation is the "standard form" equation:
... x = 7
2. The slope of the perpendicular line is the negative reciprocal of this:
... m = -1/(-1/3) = 3
In point-slope form, the equation of the perpendicular line through the given point is ...
... y = 3(x -2) +4
... y = 3x -2 . . . . . . . . simplified to slope-intercept form
3. The slope is computed from ...
... m = (change in y)/(change in x) = (-3 -4)/(-1 -(-1)) = -7/0 = undefined
The slope is undefined. This tells you the line is a vertical line. Its location is the x-value of the points, ...
... x = -1
_____
* If your point is really (77, 88), then the line has equation x = 77.
The equation of the line parallel to the y-axis that passes through the point (77,88) is x = 77
The equation of the line which is perpendicular to the line y= โ 1/3 x+6 through the point (2,4) is y = 3x - 2
The slope of the line passing through the points (โ1, 4), (โ1, โ3) is undefined.
The equation of the line is x = -1 and the graph is plotted below
The slope-intercept form of the equation of a line is:
y ย = ย mx ย + ย c
where m is the slope
c is the y-intercept
For the line parallel to the y-axis and passing through the point (77, 88)
Since the line is parallel to the y-axis, the slope is infinity and the equation is of the form x = k
Therefore, the equation of the line parallel to the y-axis that passes through the point (77,88) is x = 77
The equation of the line which is perpendicular to the line y= โ 1/3 x+6 through the point (2,4).
The slope of ย the line perpendicular to y= โ 1/3 x+6 ย is m = 3
The point-slope form of the equation of a line is:
[tex]y - y_1 = m(x - x_1)\\y - 4 =3(x - 2)\\y = 3x -6}+4\\y = 3x-2[/tex]
The slope of the line passing through the points (โ1, 4), (โ1, โ3) is calculated as:
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{-3-4}{-1-(-1)} \\m = \infty[/tex]
The slope of the line is undefined
The equation of the line is: x = -1
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