Algebra 1

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Forms of Linear Equations
Algebra 1 Section 5.6 Point-Slope Form of the
Equation of a Line
Slope-Intercept Form y mx b
Standard Form Ax By C
Point-Slope Form y y1 m(x x1)
when given a point and a slope, this is another
way to get the equation of the line
Write the equation of the line that passes
through the point and has the given slope. Then
rewrite the equation in slope-intercept form.
(x1,y1)
1. (2,4), m 3
y y1 m(x x1) (point-slope form)
y 4 3(x 2) substitute in for x1 and y1 y
4 3x 6 distributive property (get in
slope-intercept form) 4 4
y 3x 2
3
Write the equation of the line that passes
through the point and has the given slope. Then
rewrite the equation in slope-intercept form.
(x1,y1)
2. (-6,-2), m ½
y y1 m(x x1) (point-slope form)
y (-2) ½x (-6) substitute in for x1and
y1 y 2 ½(x 6) y 2 ½x 3
distributive property to get into slope-intercept
form -2 -2 y
½x 1
(x1,y1)
3. (0,-3), m ¾
y y1 m(x x1) (point-slope form)
y (-3) ¾(x 0) substitute y 3 ¾x
distributive property -3 -3
y ¾x 3 slope-intercept form
4
Write the equation of the line that passes
through the point and has the given slope. Then
rewrite the equation in standard form.
4. (7,-10), m -6
y y1 m(x x1) (point-slope form) y (-10)
-6(x 7) substitute y 10 -6x 42
distributive property to get in standard form
6x -10 6x -10 6x y 32
standard form
5. (-8,-12), m ¼
y y1 m(x x1) (point-slope form) y
(-12) ¼x (-8) substitute y 12 ¼(x
8) y 12 ¼x 2 distributive property -¼x
-12 -¼x -12 -¼x y -10
- 4
multiply by 4 to get rid of fraction (standard
form)
x 4y 40
5
Write the equation of the line that passes
through the two points. Final equation should be
in slope-intercept form.
choose either point and use the slope to
substitute into point-slope form
6. (0,2) , (3,-1)
(0,2), m -1
find slope
y y1 m(x x1) (point-slope form) y 2
-1(x 0) substitute y 2 -x distributive
property 2 2 y -x 2
slope-intercept form
m -1
6
Write the equation of the line that passes
through the two points. Final equation should be
in slope-intercept form.
7. (-3,4) , (8,4)
(8,4), m 0 y y1 m(x x1) y 4 0(x
8) substitute y 4 0 substitute
4 4 y 4 slope-intercept form
find slope
m 0
7
Write the equation of the line that passes
through the two points. Final equation should be
in standard form.
8. (- 4,0) , (2,-2)
find slope
y y1 m(x x1)
(point-slope form)
substitute
multiply by 3 to get rid of fraction (standard
form)
-3
-3y x 4 -x -x -x 3y 4 standard
form
8
Write the equation of the line that passes
through the two points. Final equation should be
in standard form.
9. (6,0) , (0,-3)
find slope
y y1 m(x x1) (point-slope form)
substitute
distributive property
2
multiply by 2 to get rid of fraction
2y x 6 -x -x -x 2y -6