The line joining P(7,2) and Q(-2,3) cuts the x-axis at_____?
Answer= (x,y)
find x and y
Since x increased by 9 when y decreased by 1, when y decreases 2 more to 0, x will increase 18 more, to 25.
algebraically,
the slope is -1/9, so
y = -1/9 x + c
since (7,2) is on the line,
2 = -7/9 + c
c = 25/9
y = -1/9 x + 25/9
when y=0,
-1/9 x + 25/9 = 0
x = 25
To find the x-coordinate where the line joining P(7,2) and Q(-2,3) cuts the x-axis, we need to find the point where the y-coordinate is 0 (since the x-axis has a y-coordinate of 0).
First, let's find the equation of the line passing through points P and Q using the slope-intercept form of a line: y = mx + b
The slope of the line (m) can be found using the formula: m = (y2 - y1) / (x2 - x1)
P(7,2): x1 = 7, y1 = 2
Q(-2,3): x2 = -2, y2 = 3
m = (3 - 2) / (-2 - 7)
m = 1 / -9
m = -1/9
Now, we have the slope (m) and one point (P), we can substitute these values into the slope-intercept form and solve for b:
2 = (-1/9)*7 + b
2 = -7/9 + b
2 + 7/9 = b
(18 + 7) / 9 = b
25 / 9 = b
So, the equation of the line is y = (-1/9)x + 25/9
To find the x-coordinate where the line intersects the x-axis (when y = 0), substitute y = 0 into the equation and solve for x:
0 = (-1/9)x + 25/9
(1/9)x = 25/9
x = (25/9) * 9/1
x = 25
Therefore, the line joining P(7,2) and Q(-2,3) cuts the x-axis at the point (25, 0).