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About Josh
Expertise
When I work through problems, I emphasize principles and key ideas which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponentials & Logarithms. Basic Calculus. Probability, Permutations and Combinations. Mathematical Induction. Complex numbers. Physics problems.
Experience
Experience:
I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.
Supplementary Website:
See a selection of past questions in my maths repository under "Question Archive"
Education Credentials:
Bachelor degree in Engineering Science.
"Everyone struggles with something."
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You are here: Experts > Science > Math for Kids > Basic Math > slope-intercept
Expert: Josh - 10/19/2009
Question
Write the slope-intercept form for an equation of the line perpendicular to the graph of the given equation and passing through the given point 8x-3y=7, (4,5)
Answer
Hi Evan,
The slope-intercept form for a straight line equation is y=s*x+b.
Parameters:
s represents the slope of the line (positive if it rise from left to right like /, negative if it falls from left to right like \)
b is called the y-intercept because this is the point where the line crosses the y-axis (the value of y when x=0).
Remember this: If "m" is the slope (aka gradient) of a straight line, then any line perpendicular to it must have a slope "n", such that m*n = -1. In other words, the perpendicular line has a slope of n=-1/m.
Step 1: We need to know the gradient of the given line 8x-3y=7.
Rearranging the equation as 3y=8x-7, then dividing both 3 on both sides, we obtain an equivalent equation in the slope-intercept form y=(8/3)x-(7/3). The interpretation is now quite simple, comparing with y=m*x+b, m=(8/3). This gives the slope.
Step 2: Using the fact that n=-1/m, n=-3/8. Thus, the perpendicular line is an equation of the form y=n*x+b.
Step 3: If (x=4,y=5) is a point on the perpendicular line, it must satisfy the equation y=n*x+b, where n=-3/8. So, we work out the value of "b". b = y-n*x = 5-(-3/8)*4 = 6.5
Final answer: y=-(3/8)x+6.5 is the equation of the perpendicular line in slope-intercept form.
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