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Back to Tutor Intake Assessment: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line

8.EE.B.6 Tutor Intake -- Similar Triangles and Slope-Intercept Derivation

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Grade 8·9 problems·~9 min·Common Core Math - Grade 8·container·8-ee-b-6
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A

Concepts

1

A slope triangle is formed between two points on a line by
drawing a horizontal segment (the run) and a vertical segment
(the rise) connecting them. What is the hypotenuse of this
triangle?

2

Two slope triangles are drawn on the same line, using two
different pairs of points. One triangle has legs 2 and 3; the
other has legs 4 and 6 — clearly different sizes. Why does the
similar triangles argument still guarantee both give the same
slope?

3

A line has y-intercept (0,b)(0, b) and passes through a general
point (x,y)(x, y). When constructing the slope triangle from
(0,b)(0, b) to (x,y)(x, y), what is the rise?

B

Procedures

1

A line passes through (0,0)(0, 0) and (3,2)(3, 2). Construct the slope
triangle between these two points and compute the slope
(rise/run). Write your answer as a fraction.

2

The same line from the previous problem also passes through
(6,4)(6, 4). Construct a slope triangle from (0,0)(0, 0) to (6,4)(6, 4)
and compute the slope. Write your answer as a fraction in
lowest terms.

3

A line through the origin has slope m=5m = 5. Using the
derivation y/x=my/x = m, write the equation of this line in the
form y=mxy = mx. Enter just the coefficient of xx.

4

A line has slope 2 and y-intercept (0,3)(0, 3). Using the
derivation (y−b)/x=m(y - b)/x = m, find the equation of the line in the
form y=mx+by = mx + b. Enter just the value of bb.

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