shreddinglicks said:Homework Statement
This is the point:
(6,0,-2)
Homework Equations
x = 4-2t
y = 3+5t
z = 7+4tThe Attempt at a Solution
Do I just plug in the points and see if I get matching values of t? If not, how do I go about this?
shreddinglicks said:I did try it. I'm asking if this is the right way to do this. I do not have any answers for this problem. Can you please tell me if that is the right way to do this?
shreddinglicks said:So the point does not lie on the line?
To determine if a point lies on a line in a plane, you can use the slope-intercept form of a line (y=mx+b) and plug in the coordinates of the point. If the resulting equation is true, then the point lies on the line. Another method is to use the distance formula to calculate the distance between the point and any two points on the line. If the distance is the same, then the point lies on the line.
No, a point can only lie on a line in a plane if it is directly on the line. Any points that are not directly on the line will not satisfy the equation of the line and therefore, do not lie on the line.
The equation for a line in a plane is commonly written in slope-intercept form as y=mx+b, where m represents the slope of the line and b represents the y-intercept (where the line crosses the y-axis).
The slope of a line in a plane can be found by using the formula (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are any two points on the line. This formula represents the change in y over the change in x, or the rise over run, which is the slope of the line.
Yes, a point can lie on more than one line in a plane. If a point lies on two or more lines, those lines are said to be concurrent. In this case, the point satisfies the equation of all the lines it lies on.