Given the relation x+y=5, determine a second relation that: a) intersects x+y=5 at (2,3) b)does not intersect x+y=5

Question

anonymous · Answer

Rewrite the given equation in slope-intercept form:
$$y = -x + 5$$
Thus, it's slope is -1 and it's y-intercept is (0,5).

(a) We need any intersecting line that passes through (2,3). Since any line will satisfy let me choose the one with slope 1. Now we can write the equation of the line using the given information, using the point-slope form :

$$y - 3 = x -2$$ or
$$y = x + 1$$

(b) If we choose a line that has the same slope as the given line but a different y-intercept then the two will not intersect. Just choose a different number in the slope-intercept form.