Question

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1. a line goes through the point (2,4) and has a slope of $\frac{3}{2}$. which of the following points is also on the line? circle all that apply.

a. (1,1) b. (3,7)
c. (0,2) d. (4,7)
e. (0,1) f. (0,0)

1. what is the slope of the line that goes through the points (6,4) and (8, -2)?

a. -6
b. -3
c. $-\frac{1}{3}$
d. 3

1. what is the slope of the line that goes through the points (-3,8) and (0,23)?

a. -5
b. $-\frac{23}{8}$
c. 5
d. $\frac{31}{3}$

1. if lines were drawn through the following pairs of points, which lines would have undefined slopes? circle all that apply.

a. (1,5) and (1,7)
b. (2,6) and (4,6)
c. (-3,2) and (-3, -3)
d. (1, -6) and (0, -6)
e. (0,1) and (0,10)

Explanation:

Question 7

Step1: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

For a line with slope \(m = \frac{3}{2}\) passing through \((x_1,y_1)=(2,4)\) and a general point \((x_2,y_2)\), we have \(\frac{y_2 - 4}{x_2 - 2}=\frac{3}{2}\), which implies \(2(y_2 - 4)=3(x_2 - 2)\) or \(2y_2-8 = 3x_2-6\) or \(2y_2=3x_2 + 2\)

Step2: Check each option

• Option A: For \((x_2,y_2)=(1,1)\), \(2\times1=2\) and \(3\times1 + 2=5\), \(2

eq5\)

• Option B: For \((x_2,y_2)=(3,7)\), \(2\times7 = 14\) and \(3\times3+2=9 + 2=11\), \(14

eq11\)

• Option C: For \((x_2,y_2)=(0,2)\), \(2\times2=4\) and \(3\times0+2=2\), \(4

eq2\)

• Option D: For \((x_2,y_2)=(4,7)\), \(2\times7=14\) and \(3\times4 + 2=12+2=14\)
• Option E: For \((x_2,y_2)=(0,1)\), \(2\times1=2\) and \(3\times0+2=2\)
• Option F: For \((x_2,y_2)=(0,0)\), \(2\times0=0\) and \(3\times0+2=2\), \(0

eq2\)

Step1: Apply the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Given \((x_1,y_1)=(6,4)\) and \((x_2,y_2)=(8,-2)\)
\(m=\frac{-2 - 4}{8 - 6}=\frac{-6}{2}=-3\)

Step1: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Given \((x_1,y_1)=(-3,8)\) and \((x_2,y_2)=(0,23)\)
\(m=\frac{23 - 8}{0-(-3)}=\frac{15}{3}=5\)

Answer:

D. \((4,7)\), E. \((0,1)\)

Question 8