Question

grade 8: week of 10/14, math hw - day 2
directions: show all steps of your thinking and circle final answers!
problem #1 - review from grade 7 (mild)
select all points that are on this line.
a. (0, 3)
b. (4, 2)
c. (30, 21)
d. (16, 11)
e. (-4, -5)
problem #2 - review from grade 7 (mild)
decide whether each table could represent a proportional relationship. if the relationship could be proportional, what would be the constant of proportionality?
the size a photo can be printed
width of photo (inches) height of photo (inches)
2 3
4 6
5 7
6 10
problem #3 - review from grade 7 (mild)
decide whether each table could represent a proportional relationship. if the relationship could be proportional, what would be the constant of proportionality?
the distance from which a lighthouse is visible
height of a lighthouse (feet) distance it can be seen (miles)
20 5
45 9
70 11
95 13

Explanation:

Step1: Find the equation of the line

From the graph, the line passes through the origin \((0,0)\) and the point \((2,1)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1 - 0}{2 - 0}=\frac{1}{2}\). Using the point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(0,0)\), the equation of the line is \(y=\frac{1}{2}x\).

Step2: Check each point

• For point \(A(0,3)\): Substitute \(x = 0\) into \(y=\frac{1}{2}x\), we get \(y = 0

eq3\).

• For point \(B(4,2)\): Substitute \(x = 4\) into \(y=\frac{1}{2}x\), \(y=\frac{1}{2}\times4 = 2\).
• For point \(C(30,21)\): Substitute \(x = 30\) into \(y=\frac{1}{2}x\), \(y=\frac{1}{2}\times30 = 15

eq21\).

• For point \(D(16,11)\): Substitute \(x = 16\) into \(y=\frac{1}{2}x\), \(y=\frac{1}{2}\times16 = 8

eq11\).

• For point \(E(-4,-5)\): Substitute \(x=-4\) into \(y=\frac{1}{2}x\), \(y=\frac{1}{2}\times(-4)=-2

eq - 5\).

Answer:

B. \((4,2)\)