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)

Explanation:

Step1: Find the equation of the line

From the graph, when \(x = 2\), \(y = 1\); when \(x = 7\), \(y = 6\).
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6 - 1}{7 - 2}=\frac{5}{5}=1\).
Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((2,1)\), we get \(y - 1=1\times(x - 2)\), so \(y=x - 1\).

Step2: Check each point

• For point \(A(0,3)\):

Substitute \(x = 0\) into \(y=x - 1\), we get \(y=0 - 1=-1
eq3\).

• For point \(B(4,3)\):

Substitute \(x = 4\) into \(y=x - 1\), we get \(y=4 - 1 = 3\).

• For point \(C(30,21)\):

Substitute \(x = 30\) into \(y=x - 1\), we get \(y=30 - 1=29
eq21\).

• For point \(D(16,11)\):

Substitute \(x = 16\) into \(y=x - 1\), we get \(y=16 - 1 = 15
eq11\).

• For point \(E(-4,-5)\):

Substitute \(x=-4\) into \(y=x - 1\), we get \(y=-4 - 1=-5\).

Answer:

B. \((4,3)\), E. \((-4,-5)\)