Answer:
The equation for line m is;
5y = -3x + 36
The equation of line q is;
3y = 5x + 8
Step-by-step explanation:
Looking at the diagram, firstly, we can see that while n and m are perpendicular, q and m are parallel
We should also note that the the line m and q both share the point (2,6)
Let’s try and work to get the equation of the lines
For line n, we have two points (1,-1) and (4,4)
The slope here can be obtained by the equation;
m = y2-y1/x2-x1 = (4 -(-1))/(4-1) = 5/3
Now let’s get for equation m
When two lines are perpendicular, the product of their slopes is -1
Let’s say m1 is like n slope and m2 is like m slope
m1 * m2 = -1
5/3 * m2 = -1
m2 = -3/5
So the slope of line m is -3/5
To get the equation of line m, we use the point slope form
The point to consider is (2,6)
Hence;
y-y1 = m(x-x1)
y-6 = -3/5(x-2)
5(y-6) = -3(x-2)
5y -30 = -3x + 6
5y = -3x + 6 + 30
5y = -3x + 36
Since line n and q are also parallel, then their slopes are equal. Hence, the slope of line q is also 5/3
We use the point slope form to get the equation of line q
where m = 5/3 and point = (2,6)
Thus;
y-y1 = m(x-x1)
y-6 = 5/3(x-2)
3(y-6) = 5(x-2)
3y -18 = 5x -10
3y = 5x -10 + 18
3y = 5x + 8
