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Writing Equations From Two Points

4.7.4 Writing Equations From Two Points

4.7.4 • Writing Equations From Two Points

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With a partner, use what you have learned to write an equation in each form from two points.

1.

Find the slope of the line that goes through (2,3)(2,3) and (6,−4)(6,−4).

Compare your answer: −74−74

m=y2−y1x2−x1=−4−36−2=−74m=y2−y1x2−x1=−4−36−2=−74

2.

Write the equation of the line in point-slope form that goes through (2,3)(2,3) and (6,−4)(6,−4).

Compare your answer:

Answer: y−3=−74(x−2)y−3=−74(x−2) or y+4=−74(x−6)y+4=−74(x−6)

Using the point (2,3)(2,3):

y−y1=m(x−x1)y−y1=m(x−x1)

y−3=−74(x−2)y−3=−74(x−2)

Using the point (6,−4)(6,−4):

y−y1=m(x−x1)y−y1=m(x−x1)

y−(−4)=−74(x−6)y−(−4)=−74(x−6)

y+4=−74(x−6)y+4=−74(x−6)

3.

Write the equation of the line in slope-intercept form that goes through (2,3)(2,3) and (6,−4)(6,−4). (Hint: use the equation from number 2)

Compare your answer:

Answer: y=−74x+132y=−74x+132

y−3=−74(x−2)y−3=−74(x−2)

y−3=−74x+144y−3=−74x+144

y−3=−74x+72y−3=−74x+72

y−3+3=−74x+72+3y−3+3=−74x+72+3

y=−74x+72+62y=−74x+72+62

y=−74x+132y=−74x+132

4.

Write the equation of the line in standard form that goes through (2,3)(2,3) and (6,−4)(6,−4).

(Hint: use the equation from number 3.)

Compare your answer:

Answer: 7x+4y=267x+4y=26

4(y=−74x+132)4(y=−74x+132)

4y=−7x+264y=−7x+26

4y+7x=−7x+7x+264y+7x=−7x+7x+26

7x+4y=267x+4y=26