I hope my questions are not very silly.
But here is another one I want to understand.
Write an equation in slope-intercept form of the line satisfying the following conditions.
through (6,7); perpendicular to x=2
My answer was 7/6(X)+2
But in truth the real answer is only y=7
How did they come to this conclusion..Is it just me making things hard on my self?
Any equation of the form x = k , is a vertical line
any equation of the form y = c, is a horizontal line
so you were given x=2 which is vertical
so your new line is horizontal and must by
y = c
look at the y value of the given point, it is 7
so y = 7
No actual work required here.
So the Y=7 is the line perpendicular to the vertical like 2 right?
The equation you provided, y = (7/6)x + 2, is not the correct answer for a line that is perpendicular to x = 2 and goes through the point (6, 7). The correct equation is indeed y = 7.
To understand why, let's break down the problem step by step:
1. The equation x = 2 represents a vertical line passing through the x-coordinate 2. In other words, no matter what the y-coordinate is, x will always be equal to 2. Therefore, the slope of this line is undefined, as there is no change in the x-coordinate.
2. For a line to be perpendicular to x = 2, it must have a slope that is the negative reciprocal of the undefined slope. The negative reciprocal of 0 (the undefined slope) is any non-zero value (including positive or negative infinity).
3. Since the line is perpendicular to x = 2 and passes through the point (6, 7), we know its slope is undefined, and the line must be a vertical line passing through the x-coordinate 6, as that is the x-coordinate of the given point (6, 7).
4. A vertical line passing through a specific x-coordinate is given by the equation x = c, where c is the x-coordinate. In this case, the equation is x = 6.
5. Now, to express the equation in slope-intercept form (y = mx + b), we would need the slope and the y-intercept. However, since the line is vertical, its slope is undefined, and it does not intersect the y-axis (no y-intercept). Therefore, we are left with just the equation x = 6.
So, the correct equation in slope-intercept form for the line that is perpendicular to x = 2 and goes through the point (6, 7) is y = 7.