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Slope is defined as the steepness of a line. Which of the following is a way to remember slope? Run over Rise Slow over Fast Fast over Slow Rise over Run If slope is equal to rise over the run, what is the slope of the line? -2/3 2/3 -3/2 3/2 Rise = -3 Run =+2 If slope is equal to rise over the run, what is the slope of the line? Rise =+5 Run=+3 3/5 5/3 -3/5 -5/3 Find the slope of the line. -1/2 2 -2 1/2 Find the slope of the line. 0 slope undefined slope 10 -10 Find the slope of the line. 0 slope 3 -3 undefined slope Find the slope of the line. 4/3 -4/3 3/4 -3/4 Undefined ? Match each graph with the correct slope. Drag each. Positive ? Negative ? 0 Slope ? The slope of a line can be found only given two points as well. If two points (x1, y1) and (x2, y2) are given, the slope can be found using the slope formula, which is:
y2 - y1 x2 - x1 m = Find the slope of the line that passes through the two points (7, 2) and (-4, -6). m = x1=7, y1=2 x2 = -4, y2 = -6 y2 - y1 x2 - x1 -6-2 -4-7 = -8 8 -11 11 = Find the slope of the line that passes through the points (8, 3) and (2, 9).
9 - 3 6 2 - 8 -6 = = Find the slope of the line that passes through the points (7, -3) and (-4, 5).
5 - (-3) -4 - 7 -11 = Find the slope of the line that passes through the two points (-2, 8) and (10, -4).
-4 - 8 -12 10 - (-2) 12 = = Find the slope of the line that passes through the points (3a - 1, a + 1) and (a + 5, 2a - 3).
(2a - 3) - (a + 1) 2a - 3 - a - 1 a - 4 (a + 5) - (3a - 1) a + 5 - 3a + 1 -2a + 6 = = Find the slope of the line that passes through the points (3a - 1, a + 1) and (5a + 2, 2a + 1).
(2a + 1) - (a + 1) 2a + 1 - a - 1 a (5a + 2) - (3a - 1) 5a + 2 - 3a + 1 = = Remember, m/m = 1. Find the slope of the line that passes through the points (-3a, 7a) and (4a, 9a). m= Find the slope of the line that passes through the points (8, 6) and (-3, -3). Notice that the coordinates of a point on the x-axis will be (#, 0), where # stands for any number. Also notice the coordinates of a point on the y-axis will be (0, #), where # stands for any number. ? (0, -2) y-int (3, 0) x-int If given an equation, you can then substitute 0 in for x when trying to find the y-intercept and also substitute 0 in for y when trying to find the y-intercept. Find the x-intercept: 3x - 5(0) = 30 3x = 30 x = 10 Given: 3x - 5y = 30 Find the y-intercept: 3(0) - 5y = 30 -5y = 30 y = -6 Find the x-intercept: 2x + 3(0) = -18 2x = -18 x = Given: 2x + 3y = -18 Find the y-intercept: 2(0) + 3y = -18 3y = -18 y = Find the x-intercept and y-intercept from the graph. x = y = Find the x-intercept and y-intercept of the given equation. x = Given: 4x - 5y = 60 y = When solved for y, a linear equation will be in the form y = mx + b. Remember, m is the slope! What is the slope of the equation y = -4x + 8? The slope of y = -4x + 8 is -4. m What is the slope of the linear equation?
y = 2 x - 6 The slope of y = 2 x - 6 is m What is the slope of the linear equation?
y = 3/4 x + 9 m = Solve the equation 3x - 2y = -6 for y and then state the slope of the line.
3x - 2y = -6 -3x -3x -2y = -3x - 6 dvide by -2 y = 3/2x + 3
The slope is 3/2. Solve the equation -x + 2y = 10 for y and then state the slope of the line.
-x + 2y = 10 +x +x 2y = x + 10 Divide by 2 y = 1/2 x + 5
The slope of the line is The standard form of a linear equation is Ax + By = C. Change y = -4x - 7 into standard form.
y = -4x - 7 +4x +4x
4x + y = -7 Change the equation y = 6x - 2 into standard form.
y = 6x - 2 -6x -6x
-6x + y = -2 Change the equation y = 5x - 4 into standard form.
y = 5x - 4 -5x -5x
+ y = -4 You are now finished with your slope tutorial.
Wasn't hard, was it! |