What is the slope of a line that is perpendicular to a line with an undefined slope?
If a line has an undefined slope (its slope is infinite), then it is a vertical line. A line that is perpendicular to a vertical line is a horizontal line, and a horizontal line has a slope of 0.
If a line has an undefined slope, it means that it is a vertical line. A vertical line is perpendicular to a horizontal line, which has a slope of 0. Therefore, the slope of a line that is perpendicular to a line with an undefined slope is 0.
To understand the slope of a line that is perpendicular to a line with an undefined slope, let's first review some basic concepts.
The slope of a line is a measure of its steepness and is denoted by the letter "m." It describes how the y-coordinate of a point on the line changes relative to the corresponding change in the x-coordinate.
In general, the slope of a line can be calculated using the formula:
m = (change in y-coordinate) / (change in x-coordinate)
The term "undefined slope" refers to a vertical line, where there is no change in the x-coordinate as we move along the line. Therefore, the denominator in the slope formula becomes zero. Division by zero is undefined in mathematics.
For a line with an undefined slope, we can say that it is a vertical line that is parallel to the y-axis. In this case, any line that is perpendicular to it will be horizontal and parallel to the x-axis.
The slope of a horizontal line is always zero. This is because there is no change in the y-coordinate as we move along the line.
So, to answer your question, the slope of a line that is perpendicular to a line with an undefined slope is zero.
What is the equation of a line that is parallel to the line y=4 that passes through the point (-32, 96)?
What is the equation of a line that is parallel to the line y=4 that passes through the point (-32, 96)?
x=-32
y=-32
x=96
y=96
To find the equation of a line that is parallel to the line y = 4 and passes through the point (-32, 96), we can determine the equation using the point-slope form.
Since the line is parallel to y = 4, the slope of the parallel line will also be 0, as mentioned earlier. Therefore, the equation of the line will have the form y = b, where b is the y-intercept.
To find the value of b, we can substitute the coordinates of the given point (-32, 96) into the equation y = b:
96 = b
Therefore, the equation of the line that is parallel to y = 4 and passes through the point (-32, 96) is y = 96.
So, the correct answer is y = 96.