Solve 20 points write the equation of line in slope-intercept form. line parallel to the y-axis that passes through the point (77,88) find the equation of the line which is perpendicular to the line y= − 1/3 x+6 through the point (2,4). find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (−1, 4), (−1, −3)

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= − 1/3 x+6 through the point (2,4) is y = 3x - 2

The slope of the line passing through the points (−1, 4), (−1, −3) 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   =  mx  +  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= − 1/3 x+6 through the point (2,4).

The slope of  the line perpendicular to y= − 1/3 x+6  is m = 3

The point-slope form of the equation of a line is:

The slope of the line passing through the points (−1, 4), (−1, −3) is calculated as:

The slope of the line is undefined

The equation of the line is: x = -1

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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.

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step-by-step explanation: hope u get it right