What is the solution with steps---**Source Information:**
8th GRADE MATH WORKBOOK
TEST 90 - Slope, Parallel Lines and Perpendicular Lines
Page Number: 100
**Question 1:**
Question Stem: What is the slope of the line that passes through the points (4, 9) and (5, 6)?
Options:
A) 4/3
B) 3/4
C) 2/3
D) -3
**Question 2:**
Question Stem: What is the slope of the line that passes through the points (7, 2) and (-3, 4)?
Options:
A) -1/5
B) 2/5
C) 5/2
D) -5/2
**Question 3:**
Question Stem: What is the slope of the line that passes through the points (2sqrt(2), 2sqrt(3)) and (3sqrt(2), 2sqrt(27))?
Options:
A) sqrt(2)
B) sqrt(3)
C) 2sqrt(2)
D) 2sqrt(6)
**Question 4:**
Question Stem: What is the slope of the line that passes through the points (8, 6) and (9, 9)?
Options:
A) 3
B) 1/2
C) -1/2
D) -1
**Question 5:**
Question Stem: What is the equation of the line through the point (6, 8) that has a slope of 3?
Options:
A) y=5x+14
B) y=14x+6
C) y=6x-23
D) y=3x-10
**Question 6:**
Question Stem: What is the equation of the line through the point (7, 3) that has a slope of -2?
Options:
A) y=6x-16
B) y=6x-14
C) y=6x-39
D) y=-2x+17
**Question 7:**
Question Stem: Line m1 has the equation y=-3x+8. Line m2 is parallel to m1 and passes through the point (6, 2). What is the equation of m2?
Options:
A) y=-3x+16 (Circled)
B) y=-3x+20
C) y=2x+8
D) y=-2x+13
**Question 8:**
Question Stem: Line m1 has the equation y=sqrt(2) + 2x. Line m2 is parallel to m1 and passes through the point (6, 9). What is the equation of m2?
Options:
A) y=sqrt(3)x + 2sqrt(3) - 1
B) y=7-2x
C) y=sqrt(3)x + 2sqrt(3)
D) y=2x-3 (Circled)
**Question 9:**
Question Stem: y=4+14x. What is the slope of the question?
Options:
A) -4
B) 4
C) 14 (Circled)
D) -14
**Question 10:**
Question Stem: 6x+8y+22=0. What is the slope of the question?
Options:
A) 7
B) -7/9
C) 9
D) -3/4 (Marked with a check or box)
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The slope of a line measures how steep it is. We calculate slope using the formula m equals y2 minus y1 over x2 minus x1. Let's solve the first problem: find the slope through points (4, 9) and (5, 6). Substituting into our formula: m equals 6 minus 9 over 5 minus 4, which equals negative 3 over 1, or negative 3. The answer is D.
Let's solve question 2: find the slope through points (7, 2) and (-3, 4). Using our slope formula, m equals 4 minus 2 over negative 3 minus 7. This gives us 2 over negative 10, which simplifies to negative 1 over 5. Notice the negative slope means the line goes downward from left to right. The answer is A.
Now let's learn the point-slope form to write equations of lines. The formula is y minus y1 equals m times x minus x1. For question 5, we have point (6, 8) and slope 3. Substituting: y minus 8 equals 3 times x minus 6. Distributing: y minus 8 equals 3x minus 18. Adding 8 to both sides: y equals 3x minus 10. The answer is D.
Parallel lines have the same slope. For question 7, line m1 has equation y equals negative 3x plus 8, so its slope is negative 3. Line m2 is parallel to m1, so it also has slope negative 3. Using point-slope form with point (6, 2): y minus 2 equals negative 3 times x minus 6. Simplifying: y equals negative 3x plus 20. The answer is B.
For our final example, let's find the slope from standard form. When an equation is written as Ax plus By plus C equals 0, the slope equals negative A over B. For question 10, we have 6x plus 8y plus 22 equals 0. Here A equals 6 and B equals 8, so the slope is negative 6 over 8, which simplifies to negative 3 over 4. The answer is D.