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Two lines are parallel if they have the same slope because parallel lines maintain a constant distance from one another and never intersect. The slope indicates the steepness and direction of the line; if two lines share the same slope, they rise or fall at the same rate. The y-intercept, however, determines where a line crosses the y-axis. If two lines have the same slope but different y-intercepts, they will never meet, thus confirming their parallel nature.
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How do you write an equation of parallel lines in slope-intercept form?
To write an equation of parallel lines in slope-intercept form (y = mx + b), first identify the slope (m) of the line you want to be parallel to, as parallel lines have the same slope. Then, choose a y-intercept (b) for the new line—this can be any value. Substitute the slope and the chosen y-intercept into the slope-intercept form to get the equation of the parallel line. For example, if the original line is y = 2x + 3, a parallel line could be y = 2x + 1.
What is the slope of a line parallel to 3 X plus 5y 15?
It will have the same slope but with a different y intercept
What is the slope of a line parallel to -8x plus y 2?
If you mean: -8x+y = 2 then y = 8x+2 and the line parallel to it will have the same slope of 8 but with a different y intercept.
What is the equation of y-intercept equals 6 and parallel to y equals x-2?
8
What is the slope of a line that has a y-intercept but no x-intercept?
A line with a y-intercept but no x-intercept will be a straight line parallel to the x axis. It will have a slope of zero.
Do parallel lines have the same slope and y intercept?
Parallel lines have the same slope, which makes them parallel. However, they cannot have the same y intercept, or else it would be the same line.
How do you write an equation of parallel lines in slope-intercept form?
To write an equation of parallel lines in slope-intercept form (y = mx + b), first identify the slope (m) of the line you want to be parallel to, as parallel lines have the same slope. Then, choose a y-intercept (b) for the new line—this can be any value. Substitute the slope and the chosen y-intercept into the slope-intercept form to get the equation of the parallel line. For example, if the original line is y = 2x + 3, a parallel line could be y = 2x + 1.
What is the slope of a line parallel to 4x y -1?
5
What are lines called that have the same slope and the same y intercept?
parallel lines.
What is the slope of the line parallel to -3x 5y 17?
It will have the same slope but a different y intercept
Write equation in slope intercept form for the line parallel to y equals 3x-3 and with a y intercept of -4?
Since the two lines are parallel, then they have the same slope, 3. Thus, the equation of the line with y-intercept -4, and parallel to y = 3x - 3 is y = 3x - 4.
What is the relationship between the equations of parallel lines?
They have the same slope. If you write the lines in the slope-intercept form, you will get, for each line: y = ax + b where a is the slope, and b is the y-intercept (where the line crosses the y-axis). For two or more parallel lines, the coefficient "a" will be the same.
Write an equation in slope intercept form for the line parallel to y equals -3 and with a y intercept of 7?
The line 'Y = - 3' has a slope of zero. Any line parallel to it also has a slope of zero. The line parallel to it with a Y-intercept of 7 is: Y = 7
What is the slope of a line parallel to the equation y equals 6x-3?
9
What is the slope of a line parallel to 3 X plus 5y 15?
It will have the same slope but with a different y intercept
What is the slope of a line parallel to -8x plus y 2?
If you mean: -8x+y = 2 then y = 8x+2 and the line parallel to it will have the same slope of 8 but with a different y intercept.
What is the equation of y-intercept equals 6 and parallel to y equals x-2?
8
