The provided reference focuses on graphing lines in slope-intercept form (y = mx + b), rather than intercept form. Let's clarify what intercept form is and how to graph it.
Intercept form of a linear equation is given by:
x/a + y/b = 1
where 'a' is the x-intercept and 'b' is the y-intercept.
Steps to Graph using Intercept Form:
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Find the x-intercept: Set y = 0 in the equation x/a + y/b = 1. This simplifies to x/a = 1, therefore x = a. The x-intercept is the point (a, 0).
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Find the y-intercept: Set x = 0 in the equation x/a + y/b = 1. This simplifies to y/b = 1, therefore y = b. The y-intercept is the point (0, b).
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Plot the intercepts: Plot the points (a, 0) and (0, b) on the coordinate plane.
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Draw the line: Draw a straight line through the two plotted points. This line represents the graph of the equation.
Example:
Let's say you have the equation x/2 + y/3 = 1.
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X-intercept: x/2 + 0/3 = 1 => x/2 = 1 => x = 2. So, the x-intercept is (2, 0).
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Y-intercept: 0/2 + y/3 = 1 => y/3 = 1 => y = 3. So, the y-intercept is (0, 3).
Plot the points (2, 0) and (0, 3) and draw a line through them.
Graphing lines in Slope-Intercept Form (y=mx+b)
The YouTube video excerpt explains how to interpret slope (m) as rise over run (change in y / change in x). If the slope is negative, like -3, think of it as a "rise" of -3, which means going down 3 units for every 1 unit you move to the right. The 'b' in the equation gives you the y-intercept (0,b).
