Lines r,s, and t are concurrent. The equation of line r is x=5, and the quation of line s is y=-2. Which could be the equation of line t?
A. y= x-7 C. y= x+3
B. y= x-3 D. y=x+7
the point (5,-2) must be on the line.
So, which equation is satisfied by that point?
To determine the equation of line t, we need to understand the concept of concurrent lines. Concurrent lines are lines that intersect at a single point. In this case, lines r, s, and t are concurrent lines.
The equation of line r is x = 5, which means that all the points on line r have an x-coordinate of 5. This is a vertical line that passes through the point (5, y) for any y-value.
The equation of line s is y = -2, which means that all the points on line s have a y-coordinate of -2. This is a horizontal line that passes through the point (x, -2) for any x-value.
Since lines r and s intersect at a single point, the equation of line t should also pass through this point. To find this point of intersection, we need to find the coordinates where lines r and s intersect.
Since line r is x = 5, any point that lies on both lines r and s must satisfy the equations x = 5 and y = -2. The only point that satisfies both equations is (5, -2).
Now, let's evaluate the answer choices to determine the equation of line t.
A. y = x - 7
If we substitute x = 5 into this equation, we get y = 5 - 7 = -2. Since this equation passes through the point (5, -2), it could be the equation of line t.
B. y = x - 3
If we substitute x = 5 into this equation, we get y = 5 - 3 = 2. Since this equation does not pass through the point (5, -2), it is not the equation of line t.
C. y = x + 3
If we substitute x = 5 into this equation, we get y = 5 + 3 = 8. Since this equation does not pass through the point (5, -2), it is not the equation of line t.
D. y = x + 7
If we substitute x = 5 into this equation, we get y = 5 + 7 = 12. Since this equation does not pass through the point (5, -2), it is not the equation of line t.
Therefore, the equation that could represent line t is y = x - 7 (option A).