1. ## Linear Relationships

Just brushing up on my linear relationships skills before an upcoming assessment task, any help would be much appreciated.

1) (6,3) is the midpoint of the line joining the points (-4, y) and (x, -6). The value of x + y is?

2) The straight line with equation ax + by = c passes through the points (2, 4) and (-3, 1). Find the values of a, b and c.

2. ## Re: Linear Relationships

Originally Posted by Fratricide
Just brushing up on my linear relationships skills before an upcoming assessment task, any help would be much appreciated.

1) (6,3) is the midpoint of the line joining the points (-4, y) and (x, -6). The value of x + y is?

2) The straight line with equation ax + by = c passes through the points (2, 4) and (-3, 1). Find the values of a, b and c.
Why don't you post some of your own work?

4. ## Re: Linear Relationships

So you do not know how to find the "midpoint of the line segment with endpoint $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$? It is given by $\displaystyle \left(\frac{x_1+ x_2}{2}, \frac{y_1+ y_2}{2}\right)$. Can you start now?

For 2, put x= 2, y= 4 into the equation to get 2a+ 4b= c, then do the same with x= -3, y= 1 to get -3a+ b= c. That gives two equations to solve for a, b, and c. Of course, there is no single solution. If a, b, c satisfy this so does any multiple.

5. ## Re: Linear Relationships

I did know about that formula for the midpoint, but was unsure on how to use it specifically for this question. However, after realising that two points are equal whenever their corresponding coordinates are the same, I was able to solve that question embarrassingly easily.

As for the second question, how would I go about solving for a, b and c? As you said, there is no single solution, but how would I get an integral solution? (I remember the text book had an integral answer, but I don't have it on me at the moment.)