How to Write the equation of a Linear Function whose Graph has a Line that has a Slope of (-5/6) and passes through the point (4,-8)

The equation for a line is of the form y=mx+b, where m represents the slope and b represents the intersection of the line with the the y-axis. This article will show by an example how we can write an equation for the line that has a given slope and passes through a given point.

    We will find the Linear Function whose graph has a slope of (-5/6), and passes through the point (4,-8). Please click on the image to see the graph.

    In order to find the Linear Function, we will use the Slope-Intercept form, which is y=mx+b. M is the slope of the line, and b is the y-intercept. We already have the slope of the line, (-5/6), and so we will replace m with the slope. y=(-5/6)x+b. Please click on the image for a better understanding.

    Now, we can replace x and y with the values from the point that the line goes through, (4,-8). When we replace x with 4 and y with -8, we get -8=(-5/6)(4)+b. By simplifying the expression, we get -8=(-5/3)(2)+b. When we multiply (-5/3) by 2, we get (-10/3). -8=(-10/3)+b. We will add (10/3) to both sides of the equation, and by combining like terms, we get: -8+(10/3)=b. In order to add -8 and (10/3), we need to give -8 a denominator of 3. To do this, we mulitply -8 by (3/3), which equals -24/3. We now have (-24/3)+(10/3)=b, which is equal to (-14/3)=b. Please click on the image for a better understanding.

    Now that we have the value for b, we can write the Linear Function. When we replace m with (-5/6) and b with (-14/3) we get: y=(-5/6)x+(-14/3), which is equal to y=(-5/6)x-(14/3). Please click on the image for a better understanding.

About the Author

Zadock Reid began writing professionally in 2008, with work appearing on eHow and several other websites. He is listed in "Who's Who Among America's Teachers." He holds a Bachelor of Arts in history from Andrews University in Michigan, a Master of Science in mathematics from the University of Illinois-Chicago and a Ph.D. in mathematics from Sussex College in Sussex, England.

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