Question

19

A
Straight line A passes through the points (-1, 2) and (1,6)
Straight line B has equation y-x
Work out the coordinates of the point where line A crosses line B
You may use the grid to help you.
40
10
+
7
-2
14
T
6
5-
4-
3
2
O
-1-
-2-
-3
-5-
-6-
Answer (
2
3
5
6
[4 marks]

Answer 1

To find the coordinates where line A crosses line B, we need to find the point where the equations of the two lines intersect. Line A passes through the points (-1, 2) and (1, 6), and line B has the equation y - x.

First, let's find the equation of line A using the two given points:

Calculate the slope (m) of line A:
m = (y2 - y1) / (x2 - x1)
m = (6 - 2) / (1 - (-1))
m = 4 / 2
m = 2
Use the point-slope form of a line to write the equation of line A:
y - y1 = m(x - x1)
Taking (-1, 2) as a point on line A:
y - 2 = 2(x - (-1))
y - 2 = 2(x + 1)
y - 2 = 2x + 2
y = 2x + 4
Now we need to find the point where line A (y = 2x + 4) crosses line B (y - x).
Substitute y = 2x + 4 into the equation y - x:
2x + 4 - x = 0
x + 4 = 0
x = -4

Substitute the value of x into the equation of line A to find the corresponding y-coordinate:
y = 2x + 4
y = 2(-4) + 4
y = -8 + 4
y = -4

Therefore, the coordinates of the point where line A crosses line B are (-4, -4).