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Suppose the equation of the line is y = mx c where m is not zero.Then the x-intercept is (-c/m, 0) and the y-intercept is (0, c)
Therefore -c/m + c = k
multiplying by m, -c + cm = km
or c*(m -1) = km
and so, provided (m - 1) is not 0, c = km/(m - 1)
and the equations of the line are y = mx + km/(m - 1) for different values of m.
When m - 1 = 0, then m = 1 and so the equations are y = x + c so that the intercepts are (-c, 0) and (0, c) and so 2*c = k so the equation is y = x + k/2
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How many solutions are there when two lines have different slopes and y-intercepts?
If they are straight lines, then one solution.
How do you use the slopes and y-intercepts to determine if two lines coincide or are parallel?
If the slopes are different the lines are neither - they intersect. They are parallel or coincident if the slopes are the same. Then, if the y-intercepts are the same they are coincident while if the y-intercepts are different, they are parallel.
Lines with the same slope are?
Lines with the same slope but with different y intercepts are parallel.
Which of these are characteristics of two lines that coincide?
Same slope and intercepts
Different interceps are characteristics of two parallel lines?
Yes, parallel lines have different intercepts
