Page 345 - Algebra 1

Point-Slope Form
The form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line is called the point-slope form of a line.
Example
2
Writing an Equation in Point-Slope Form
Write the equation of a line that has a slope of 3 and passes through point (2, 4) in point-slope form.
SOLUTION
y - y1 = m(x - x1) Write the formula.
y - 4 = 3(x - 2) Substitute (2, 4) for (x1, y1) and 3 for m.
Writing an Equation Using Two Points
Write the an equation of a line that passes through the points (1, -3) and (4, 5) in slope-intercept form.
Example
3
SOLUTION
_y 2 - y 1 m=_ x2 - x1
m = 5 - (-3) 4-1
= _8 3
T h e s l o p e i s = _8 . 3
y - y1 = m(x - x1)
Write the slope formula.
Substitute (1, -3) for (x1, y1) and (4, 5) for (x2, y2). Simplify.
Write the point-slope formula.
Hint
You can substitute either (1, -3) or (4, 5) for (x1, y1).
y-5=_8(x-4) 33
3 ( y - 5 ) = 3 · _8 ( x - 4 ) 3
Check
__ Graphy= 8x- 17.
Thegraphof y=_8x-_17 appearstogo 33
through the points (1, -3) and (4, 5).
3y - 15 = 8x - 32 __
Distribute the 3 and 8. Solvefory.
y= 8x- 17 33
Substitute(4,5)for(x1,y1)and_8 form. M u l t i p l y b o t h s i d e s b y 3 .
(4, 5)
33
330 Saxon Algebra 1
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