Discuss whether a vertical line ever has a Y intercept
A vertical line does not have a Y intercept because a Y intercept is the point at which a line crosses the Y axis, and a vertical line does not cross the Y axis at any point. A vertical line is parallel to the Y axis and extends indefinitely upwards and downwards without intersecting the Y axis. Therefore, its equation cannot be written in the form y = mx + b, where b is the Y intercept. However, the equation of a vertical line can be expressed as x = constant, where constant is the x-coordinate of any point on the line.
Find the slope and y- intercept of the line -9x+4y=20
To find the slope and y-intercept of the line -9x + 4y = 20, we need to rearrange it into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Starting with -9x + 4y = 20:
1. Add 9x to both sides to isolate the y-term:
-9x + 4y + 9x = 20 + 9x
4y = 9x + 20
2. Divide both sides by 4 to solve for y:
y = (9/4)x + 5
Now we can see that the slope, m, is 9/4 and the y-intercept, b, is 5.
So the slope is 9/4 and the y-intercept is (0, 5).
Line 1 goes through (0,4) and (8,0)
Line 2 goes through (0,-8) and (4,0)
To determine whether Line 1 and Line 2 are parallel, perpendicular, or neither, we need to find the slopes of each line by using the slope formula:
slope = (change in y) / (change in x)
Line 1:
slope = (0 - 4) / (8 - 0) = -4/8 = -1/2
Line 2:
slope = (0 - (-8)) / (4 - 0) = 8/4 = 2
To determine the relationship between these lines, we can compare their slopes:
- If the slopes are equal, the lines are parallel.
- If the slopes are negative reciprocals, the lines are perpendicular.
- If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
The slope of Line 1 is -1/2, and the slope of Line 2 is 2. These slopes are neither equal nor negative reciprocals, so Line 1 and Line 2 are neither parallel nor perpendicular.
One of the top 10 occupations in terms of job growth in the next few years is expected to be physician assistants. The number of people, y, in thousands, employed as physician assistants in a country can be estimated by linear equation 32x-5y=-365, where X is the number of years after 2008
To solve this problem, we want to rearrange the equation 32x - 5y = -365 into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. This will give us a better understanding of the relationship between the number of years after 2008 (x) and the number of people employed as physician assistants (y).
Starting with 32x - 5y = -365:
1. Subtract 32x from both sides to isolate the y-term:
-5y = -32x - 365
2. Divide both sides by -5 to solve for y:
y = (32/5)x + 73
Now we can see that the slope, m, is 32/5 and the y-intercept, b, is 73.
This means that for every additional year after 2008, the number of people employed as physician assistants is expected to increase by 32/5 thousand (or 6.4 thousand) on average. The y-intercept tells us that in 2008 (when x = 0), there were expected to be 73 thousand people employed as physician assistants in the country.
The poor phone company has learned that my pricing a newly released fun noodle at two dollars sales were reach 8000 fun noodles per day during the summer raising the price to three dollars. We’ll call the sales so far to 6000 fun noodles per day assume that the relationship between sale, price, eggs and number of fun noodles sold why is linear write an equation in slope intercept form describe in this relationship
It seems that some information may be missing from the problem description, particularly regarding the relationship between sales, price, and eggs as it relates to the number of fun noodles sold. Without this information, we cannot answer the question as written.
Please provide additional details or clarification on the problem, and I will do my best to help you solve it.