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Write the Equation of a line that passes through (4,7) and has slope of -3/4

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2 Answers

Hi Andrew;
The point-slope formula is as follows...
y-y1=m(x-x1)
m=slope
Let's plug-in...
y-7=(-3/4)(x-4)
y-7=[(-3/4)(x)]+3
Let's add 7 to both sides of the equation...
7+y-7=[(-3/4)(x)]+3+7
y=(-3/4)x+10
 
Try this: 
 
Slope intercept form is y = mx + b ;  m = slope.
 
y = -3/4x +b
 
If it passes through (4,7), plug those numbers in, 4 for x and 7 for y to find b (the constant)
 
7 = -3/4 (4) + b
7 = -3 + b   Remember -3/4 * 4 = -3/4 * 4/1 (whole number converts to fraction by dividing by 1)
 
Add 3 to each side to get your constant "b".
 
b = 10
 
y = -3/4 x + 10
 
Knowing the slope intercept form is faster than figuring it out from the definition of slope.  Slope requires knowing 2 points, not just one.  The slope intercept form is easier to memorize and requires only two pieces of information - the slop and ONE point on the line.

Comments

The question requires the point-slope formula, not slope-intercept.  Your answer will result in a failing grade because Andrew would be disobeying the instructor.
 

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