point slope equation of a line. any time you are given the slope of a line (m) and a point on the...
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Point Slope Equation of a Line
Point Slope Equation of a Line
Any time you are given the slope of a line (m)and a point on the line ( x1, y1 )
Use the point-slope equation of a line to solve.
y – y1 = m ( x – x1 )
Point Slope Equation of a Line
m = 5; ( 2, 3 )
Use the point-slope equation of a line to solve.
y – y1 = m ( x – x1 )
y – 3 = 5 ( x – 2 )
Slope-intercept Equation of a Line
y – 3 = 5 ( x – 2 )y – 3 = 5x – 10
y = 5x – 7
This is the slope-intercept equation of the line with a slope of 5 passing through the point ( 2,
3 )
Standard Equation of a Line
y = 5x – 7 This is the slope-intercept equation of the line
with a slope of 5 passing through the point ( 2, 3 )
If they want the answer in standard formAx + By = C
just rearrange the furniture!
- 5x + y = -7
A matter of style
- 5x + y = -7
Some textbook authors dislike starting with a negative.
Although this is a correct answer, if it is not included in the multiple choice answers, clean it
up by multiplying everything by -1.
5x – y = 7
Oh no! A Fraction!
What if the slope is a fraction?
M = 2/3 ; ( - 7, - 5 )
We still use y – y1 = m ( x – x1 )
2( 5) [ ( 7)]
3y x
Oh no! A Fraction!
y – y1 = m ( x – x1 )
Notice how I use parentheses to keep my signs straight!
2( 5) [ ( 7)]
3y x
Clean up the double signs
2( 5) [ ( 7)]
3y x
25 [ 7]
3y x
Fractions and Equal Signs
Whenever you have a fraction and an equal sign,
multiply both sides of the equation by the LCD.
25 [ 7]
3y x
Fractions and Equal Signs
25 [ 7]
32
3( 5) 3( )[ 7]3
3 15 2 14
y x
y x
y x
Finish Up!
3 15 2 14
3 2 1
2 1
3 3
y x
y x
y x
Answer in slope-intercept form
Finish Up!
Answer in standard form with no leading negative.
3 2 1
2 3 1
2 3 1
y x
x y
x y
Point- slope equation of a line
1. If you know a point ( x1, y1 ) and the slope m.
2. Use y – y1 = m ( x – x1 )
3. Distribute the m
4. Move the y1
5. This gives the slope-intercept equation of the line.
6. If they want it in standard form, rearrange the furniture ( and you may have to clear a leading negative).
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