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5.5 Writing Equations in Point-Slope Form
• Write the equation of a line in point-slope form.
• Write linear equations in different forms
What we Know so far….What we Know so far….
Slope Intercept Form
bmxy
Where m is the slope and b is the intercept
The New Stuff… Point- Slope The New Stuff… Point- Slope FormFormPoint- Slope form is:
)( 11 xxmyy Where m is the slope
and (x1,y1) is the given point
Point Slope Form
Write the equation of the line with slope 3 and passing through the point (1, 5).
y – y1 = m(x – x1)
135 xy335 xy
533 xy
23 xy
Write the equation of the line with slope ¾ and passing through the point (-5, 3).
y – y1 = m(x – x1)
)5(3 43 xy
415
433 xy
412
415
43 xy
427
43 xy
53 43 xy
Write the equation of the line with slope -4/7 and passing through the point (2, -4).
y – y1 = m(x – x1)
2)4( 74 xy
78
744 xy
728
78
74 xy
720
74 xy
24 74 xy
Write the equation of the line passing through the points (-2, 6) and (3, -1).
y – y1 = m(x – x1)
3)1( 57 xy
55
521
57 xy
516
57 xy
521
571 xy
xym
)2(361
m
57m
Write the equation of the line passing through the points (4, 3) and (6, 8).
y – y1 = m(x – x1)
43 25 xy
3103 25 xy
725 xy
103 25 xy
xym
4638
m
25m
Write the equation of the line passing through the points (4, -3) and (-7, -1).
y – y1 = m(x – x1)
4)3( 112 xy
1133
118
112 xy
1125
112 xy
118
1123 xy
xym
47)3(1
m
112
m
112m
Why does the point-slope form work?
xym
1
1
xxyym
Find the slope between (x1, y1) and (x, y).
11 yyxxm
11 xxmyy
1xxbysidesbothmultiply
1xx 1xx
Convert y = 3x + 2 to standard form.
23 xy
23 yx
23 yx
)1(231 yx
Convert to standard form.
427
43 xy
427
43 yx
2743 yx
)4(4 427
43 yx
427
43 xy
Convert to standard form.
716
74 xy
716
74 xy
716
74 yx
1674 yx
)7(7 716
74 yx
716
74 xy
Write the equation of the line parallel the line 4x – 5y = 7 that passes through the point (-3, 7)
754 yx
745 xy
57
54 xy
54m
y – y1 = m(x – x1)
)3(7 54 xy
535
512
54 xy
547
54 xy
512
547 xy
37 54 xy
Write the equation of the line perpendicular the line
3x + 2y = 9 that passes through the point (2, 5)
923 yx
932 xy
29
23 xy
23m
y – y1 = m(x – x1)
25 32 xy
315
34
32 xy
311
32 xy
34
325 xy
32m
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