The lines k1, k2 and k3 represent three different equations as shown in thegraph below. The solution of the equations represented by the lines k1 and k3 isx = 3 and y = 0 while the solution of the equations represented by the lines k2and k3 is x = 4 and y = 1.1Which of these is the equation of the line k3?(a) x - y = 3(b) x - y = -3(c) x + y = 3(d) x + y = 1
Question
The lines k1, k2 and k3 represent three different equations as shown in thegraph below. The solution of the equations represented by the lines k1 and k3 isx = 3 and y = 0 while the solution of the equations represented by the lines k2and k3 is x = 4 and y = 1.1Which of these is the equation of the line k3?(a) x - y = 3(b) x - y = -3(c) x + y = 3(d) x + y = 1
Solution
The solution of the equations represented by the lines k1 and k3 is x = 3 and y = 0. This means that the line k3 passes through the point (3,0).
The solution of the equations represented by the lines k2 and k3 is x = 4 and y = 1. This means that the line k3 also passes through the point (4,1).
We can use these two points to find the equation of the line k3. The general form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
The slope m is given by the difference in y-coordinates divided by the difference in x-coordinates, i.e., m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (1 - 0) / (4 - 3) = 1.
The y-intercept b is the y-coordinate of the point where the line crosses the y-axis. Since the line passes through the point (3,0), we can substitute x = 3 and y = 0 into the equation y = mx + b to find b. This gives 0 = 1*3 + b, so b = -3.
Therefore, the equation of the line k3 is y = x - 3. In the form x - y = c, this becomes x - y = 3, so the correct answer is (a) x - y = 3.
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