Write an equation for the line that passes through (−8,14) and whose slope is undefined. Give an answer in standard form.
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Part 1
Write the equation in the standard form where all coefficients are expressed as relatively prime integers.
Since the slope of the line is undefined, it means that the line is a vertical line. A vertical line has the equation of the form x = a, where a is the x-coordinate of any point on the line.
In this case, the line passes through (-8,14), so the equation of the line is x = -8.
Rearranging the equation to standard form:
x + 0y = -8
The equation in standard form is 1x + 0y = -8.
To write the equation of a line that passes through the point (-8,14) and has an undefined slope, we know that the line must be vertical because undefined slope represents a vertical line.
For a vertical line passing through a point (a,b), the equation can be written in the form x=c, where c is the x-coordinate of the point.
In this case, the x-coordinate of the given point is -8.
Therefore, the equation for the line is x = -8.
However, to express the equation in standard form with all coefficients as relatively prime integers, we need to rearrange the equation so that the x and y terms are on the same side and the constant term is on the other side.
By subtracting x from both sides, we get:
x - (-8) = -8 - (-8)
Simplifying this, we have:
x + 8 = 0
Now, let's rewrite this equation in standard form by moving the x term to the other side:
x + 8 = 0
x + 8 - 8 = 0 - 8
x = -8
The equation for the line passing through (-8,14) with an undefined slope in standard form is x = -8.
To find the equation of the line passing through a point (-8, 14) with an undefined slope, we know that the line is vertical. A vertical line has an undefined slope because its rise (change in y) is infinite while its run (change in x) is zero.
Since the line is vertical, its equation will be in the form x = a, where 'a' is the x-coordinate of any point on the line. In this case, the x-coordinate is -8. Therefore, the equation of the line is:
x = -8
However, the standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A is positive.
To convert the equation x = -8 into standard form, we can multiply both sides of the equation by -1 to make the coefficient of x positive:
-1(x) = -1(-8)
-x = 8
Now, we can rewrite it in standard form by moving the x term to the left side:
x + 0y = 8
Here, A = 1, B = 0 (since there is no y-term), and C = 8. Therefore, the equation of the line in standard form is:
1x + 0y = 8
Simplifying, we get:
x = 8
So, the equation of the line passing through (-8, 14) with an undefined slope in standard form is x = 8.