Unit 2, Lesson 16
Writing Equations for Lines
Accelerated 7
16.1
Warm-up
Here are several lines.
- Match each line shown with a slope from this list: , 2, , 1, 0.25, .
- One of the given slopes does not have a line to match. Draw a line with this slope on the empty grid (F).
16.2
Activity
Line is shown in the coordinate plane.
- What are the coordinates of and ?
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Is point on line ? Explain how you know.
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Is point on line ? Explain how you know.
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Is point on line ? Explain how you know.
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Suppose you know the - and -coordinates of a point. Write a rule that would allow you to test whether the point is on line .
16.3
Activity
Here are two diagrams:
- Complete each diagram so that all vertical and horizontal sides of the slope triangles have expressions for their lengths.
- Use what you know about similar triangles to find an equation for the quotient of the vertical and horizontal side lengths of the smaller triangle in each diagram.
Student Lesson Summary
Here is a line on the coordinate plane.
Coordinate plane, x, negative 1 to 6, y negative 1 to 8. A line through point A, at 0 comma 1, point C at 1 comma 3, and point E at x comma y. A dotted line connects C to B at 1 comma 1. Another connects E to D at x comma 1. The length of E D is y minus 1. The length of A, D is x.
The points , , and are on the same line. Triangles and are slope triangles for the line, so they are similar triangles. We can use their similarity to better understand the relationship between and , which are the coordinates of point .
- The slope for triangle is because the vertical side has length 2 and the horizontal side has length 1.
- For triangle , the vertical side has length because is the distance from point to the -axis, and side is 1 unit shorter than the distance. The horizontal side has length . So, the slope for triangle is .
- The slopes for the two slope triangles are equal, meaning .
The equation is true for all points on the line.
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