Question

Determine the equation of a line to the x-axis that passes through the point(4, -1). Can you please help me understand what im suppose to do?

Answer 1

Answer:

x = 4

Step-by-step explanation:

A line perpendicular to the x-axis is a vertical line. A vertical line has the equation ...

... x = <some constant>

If you want the vertical line to go through a point with an x-coordinate of 4, then the consant must be 4.

... x = 4

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Comment on Equations of Lines

Often you will see the equation of a line written in slope-intercept form

... y = mx + b . . . . . . . slope = m; y-intercept = b

or in point-slope form

... y -k = m(x -h) . . . . . . slope = m; point = (h, k)

These work well enough when the slope is defined (that is, not "undefined"). A vertical line, one perpendicular to the x-axis (or parallel to the y-axis) has undefined slope, so cannot be written using an equation of the above form.

Another form of the equation of a line is "standard form"

... ax +by = c

where a, b, and c are integers that may be zero. When b=0, the line is a vertical line, equivalent to x = c/a. This form of the equation of a line can be used when the slope is undefined. (It can also be a useful form for other reasons, as well.)