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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
What else can I help you with?
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
How many solutions are there when two lines have different slopes and y-intercepts?
If they are straight lines, then one solution.
Which type of lines pass through points (0 0) (5 5) and (0 0) (7 1) on a grid?
They are positive straight lines that intercepts the origin and have no y intercepts.
How can you use the slopes and y-intercepts to determine if two lines are parallel?
If the lines are straight and have the same slope they are parallel, no matter what the y intercept is
What is the equetion of a straight line?
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).
What lines have the same slope and different y-intercepts?
Parallel lines
When two slopes are equal they are?
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)
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
How many lines can you draw whose y-intercepts are 0?
There are an infinite number of possible lines.
If two lines have different slopes and different y intercepts how many points of intersection are there?
If two lines have different slopes, then they intersect at exactly one point. It makes no difference what their y-intercepts are.
What is the relation between straight lines and linear equations?
The graph, in the Cartesian plane, of a linear equation is a straight line. Conversely, a straight line in a Cartesian plane can be represented algebraically as a linear equation. They are the algebraic or geometric equivalents of the same thing.
