how to find the slope of a line without given points?
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You've seen that you can find the slope of a line on a graph by measuring the rise and the run. You can also find the slope of a straight line without its graph if you know the coordinates of any two points on that line. Every point has a set of coordinates: an x-value and a y-value, written as an ordered pair (x, y).
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The point slope form of the equation of a line is given by y - y1 = m(x - x1). where (x1, y1) is a point on the line and m is the slope of the line.
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['Find the slope, m.', 'Find the y-intercept, b.', 'Plot the y-intercept.', 'Use the slope to plot additional points.', 'Draw the line.']
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This is the slope of the line (usually called m). If you need to find the equation of the line simply input all of our knowns into the slope/line formula: y-y1=m(x-x1). For the above example that's y-1=1(x-2). Then simplify and you've got y=x-1.
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To find the slope of the given line we need to get the line into slope-intercept form (y = mx + b), which means we need to solve for y: The slope of the line 3x – 5y = 9 is m = 3/5. Therefore, the slope of the line parallel to this line would have to be m = 3/5.
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['the equation of a line in slope-intercept form is. ∙y=mx+b.', 'where m is the slope and b the y-intercept. rearrange x+y=3 into this form.', 'subtract x from both sides. ⇒y=−x+3←in slope-intercept form.']
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If you think about the slope formula, y = mx + b, if m = 0, then y = 0x+b, and if you multiply anything by 0, it disappears, so zero slope gives y = b. If it is x= #, it is a vertical line through whatever value o x you have.
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How to Use the Formula and Calculate Slope. The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
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To get it more clear let us assume that ax + by + c = 0 (b ≠ 0) be the equation of the given straight line. Therefore, the slope of the straight line ax + by + c = 0 is (- ab).
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['Pick two points on the line and determine their coordinates.', 'Determine the difference in y-coordinates for these two points (rise).', 'Determine the difference in x-coordinates for these two points (run).', 'Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).']
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To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
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if you didn't have an equation, just a graph, and needed to find slope you would use the formula rise/run. Pick a point and count how far you go up the y-axis and how far you move horizontally on the x-axis. the slope would be -5 because the its in y=mx+b form where m is the slope, and b is the y-intercept.
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zero slope (when lines are horizontal) undefined slope (when lines are vertical)
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['(x1, y1) = (-2,-1)', '(x2, y2) = (4,3)', 'slope = ((y2-y1)/(x2-x1))']
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You can't find the slope of a line if only given one point. If you had a visual representation of the line such as a graph or a table you could find a second point and then use the formula for slope, y = (y2-y1) / (x2-x1). Imagine a single point on the xy graph.
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Find the Equation of a Line Given That You Know Its Slope and Y-Intercept. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
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For a curved line, slope is a concept from calculus, so it's a little hard to explain without any calculus. It turns out the the formula for the slope of: y = ax^3 + bx^2 + cx + d is 3ax^2 + 2bx + c I substitued 0 and 1 into this and set the results equal to the given slopes. -