write the standard form of the equation for the line that passes through the points (10,1) and (10,-10)

Question

how do you figure out this question? what is standard form?

Answer 1

slope-intercept form for the equation of a line is y = mx + b where m is the slope and b is the y-coordinate of the y-intercept. Some people say b is the y-intercept. It is the point where the line crosses the y-axis. All points on the y-axis have an x-coordinate of zero. Therefore the y-intercept is the point (0 , b)

 

standard form for the equation of a line is Ax + By = C

 

These forms can be changed from one to the other.

For example, y = (3/4)x + 2 with slope m = 3/4 and y-intercept = 2

Standard for is obtained by multiplying everything by 4 to eliminate the denominator and then re-arranging terms.

4y = 3x + 8

3x - 4y = -8

 

For horizontal lines (lines with a slope = 0 and parallel to the x-axis), the equation looks different.

All points on a given horizontal line have the same y-coordinate because all points are the same distance from the x-axis. We don't need to provide information about the x-coordinate because it can be any number from -∞ to ∞. We only need to say what the y-coordinate is. Therefore the equation of a horizontal line looks like this: y = b where b is the y=coordinate of every point on the line.

 

Similarly, vertical lines (lines with undefined slope and parallel to the y-axis), also have an abbreviated equation. All points on a given vertical line have the same x-coordinate because all points are the same distance from the y-axis. We don't need to provide information about the y-coordinate because it can be any number from -∞ to ∞. We only need to say what the x-coordinate is. Therefore the equation of a vertical line looks like this: x = a where a is the x=coordinate of every point on the line.

 

In this question, both points have the same x-coordinate which is 10. Therefore the equation of this vertical line is

x = 10

Answer 2

An equations for a line in standard form would be y = m·x + b, where m is the slope and b is the y-intercept.  When we try to calculate the slope of this line by using rise over run, i.e. Δy/Δx we get (-10 -1)/(10 -10) = -11/0!.  Since division by 0 is not allowed, we say that the slope of the line is "undefined", which really means that we have a vertical line passing through the point x = 10.

 

So x = 10 is our standard form equation for this line.