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Linear Equations Slope-Intercept and Standard Form
Slope-Intercept Form Any linear equation can be solved for y and written like this: This form of a linear equation is called ______-_________ form.
Slope-Intercept Form The m represents the _____ of the line. It is often convenient to write the slope as a fraction, since slope is defined as...
Slope-Intercept Form The b represents the __-__________. (Which is where the line crosses the __- _____.) It is important to pay attention to the signs of both m and b!
y = 3x - 5 Can you determine the slope and the y- intercept of this equation? The slope is ___ Which we might choose to write as ___ (to make the rise and run more obvious)
y = 3x - 5 What about the y-intercept? You didnt miss the negative sign did you? We can graph this equation by first plotting the y-intercept, then plotting a second point found via the slope!
y = 3x - 5 Could you sketch the graph? First plot the y- intercept. The rise is __. The run is __.
3x + 2y = 4 Re-write the equation in slope-intercept form. Solve for y. Put the x term first on the right side of the equation. The slope is ___ and the y-int is ___.
y = -3/2x + 2 Now graph the linear equation.
Writing a Linear Equation Suppose you were given a point on a line and a slope. Could you write the equation of the line? How could you find the y-intercept?
m = 2/3 and the line contains (-3,-2) Since we know the slope and at least one value of x and y that makes the equation true, we can simply substitute and solve!
Writing a Linear Equation Now we know both the slope and the y- intercept. Can you write the equation in both slope-intercept and standard form? Write the equation in slope-intercept form.
X and Y intercepts. X-intercept: The point where a line crosses the x-axis. The coordinates are ( x, 0) where x is any number on the x-axis Y-intercept:
WARM UP 1. Explain how to graph a linear equation written in slope-intercept form. 2. Explain how to graph a linear equation written in point-slope form.
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Warm Up Find the slope of the line that passes through each pair of points. 1. (3, 6) and (–1, 4) 2. (1, 2) and (6, 1) 3. (4, 6) and (2, –1) 4. (–3, 0)
SYSTEMS OF LINEAR EQUATIONS Solving Linear Systems Algebraically.
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EXAMPLE 1 Write an equation of a line from a graph SOLUTION m 4 – (– 2) 0 – 3 = 6 – 3 = = – 2 STEP 2 Find the y -intercept. The line intersects the y -axis.
4.7 Graphing Lines Using Slope Intercept Form Goal: Graph lines in slope intercept form.
1.4 Linear Equations in Two Variables. Definition of Slope The slope of the line through the distinct points (x 1, y 1 ) and (x 2, y 2 ) is where x 2.
Warm Up Find the slope of the line that passes through each pair of points 1.(3, 6) and (–1, 4) 2. (1, 2) and (6, 1) Course Using Slopes and Intercepts.
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First let’s review 5.1 Write the equation in slope-intercept form, given m = 3 ang b = (0,-2) Example m = 3, b = (0,-2) y = __ x + ___ y = mx + b.
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Parallel Lines. We have seen that parallel lines have the same slope.
Parallel and Perpendicular Lines. Gradient-Intercept Form Useful for graphing since m is the gradient and b is the y- intercept Point-Gradient Form Use.
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6.5 Graphing Linear Inequalities. Graphing Linear Equations A linear equation can be written in either slope-intercept form Or in standard form To graph.
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