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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

Q: What is straight lines with algebraic sum of intercepts fixed as k?

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If they are straight lines, then one solution.

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 but with different y intercepts are parallel.

Same slope and intercepts

Yes, parallel lines have different intercepts

Related questions

If they are straight lines, then one solution.

They are positive straight lines that intercepts the origin and have no y intercepts.

If the lines are straight and have the same slope they are parallel, no matter what the y intercept is

Y=mx+b. this equation is used for straight lines on a graph. Each letter represents something different. Y is the y-axis (the vertical lines of the graph). M is the slope. X is the x-axis (the horizontal lines of the graph). B is the y-intercepts (where the line intercepts with the y axis).

Parallel lines

There are two possibilities. If the y intercepts are unique, the lines are parallel. If the y intercepts are the same, the lines are coincident. ( They are the same line)

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 but with different y intercepts are parallel.

Same slope and intercepts

There are an infinite number of possible lines.

If two lines have different slopes, then they intersect at exactly one point. It makes no difference what their y-intercepts are.

They have equal slopes, equal y-intercepts, equal x-intercepts,and if they are line segments, then they have equal lengths.