Answer:
The coordinates of point p are:
x = -3.2
y = 9.6
Step-by-step explanation:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then if we know that L1 passes through the points (6, 5) and (10, 3) the slope of this line will be:
a = (3 - 5)/(10 - 6) = -0.5
Then this line will be something like:
y = -0.5*x + b
To find the value of b we can just replace the values of one of the points in the above equation. For example if we use the point (6, 5), this means that:
x = 6
y = 5
Then we get:
5 = -0.5*6 + b
5 = -3 + b
5 + 3 = b
8 = b
Then the equation for line L1 is:
y = -0.5*x + 8
Now, for line L2 we know that it has a gradient -3 (for linear equations, the gradient is the same as the slope)
Then line L2 has a slope equal to -3
y = -3*x + b
And we know that this line passes through the origin, (0, 0)
Then if we replace the values of that point in our equation, we get:
0 = -3*0 + b
0 = b
Then line L2 is:
y = -3*x
Then our two lines are:
y = -0.5*x + 8
y = -3*x
Now we want to find the point where these lines intersect. The lines will intersect in one point that belongs to both lines, then we can use the relation:
-0.5*x + 8 = y = -3*x
-0.5*x + 8 = -3*x
now we can solve this for x.
-0.5*x + 8 = -3*x
8 = -3*x + 0.5*x
8 = -2.5*x
8/-2.5 = x = -3.2
Now we need to evaluate one of the lines on this value, i will use line L2
y = -3*(-3.2) = 9.6
Then we can conclude that the lines do intersect in the point:
x = -3.2
y = 9.6
this point is written as: (-3.2, 9.6)
