ST. THERESE ACADEMY & IMDII
TOMAS CABILI, ILIGAN CITY
063-223-1487
MATHEMATICS 8
WEEK 9
FIRST QUARTER
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PT:
NAME:
SCORE:
GRADE/SECTION:
SUBJECT TEACHER: HANNAH JANE G. CLERIGO
Objectives: After going through this lesson, you are expected to find the equation of a line given
(a) two points, (b) the slope and a point and (c) the slope and its intercepts.
WHAT I NEED TO KNOW
You can find the equation of the line given the graph, 2 points, slope and a point, slope and
intercept or the x and y-intercepts.
A. Given the slope and the y– intercept.
Remember that equation of the line can be written in the form of slope intercept form, 𝒚 = 𝒎𝒙 + 𝒃
Example: If m = 2 and the y-intercept b = -3, the equation is y = 2x - 3.
This can be changed to standard for of equation: -2x + y = -3.
B. Given 2 points.
The formula in finding the equation of the line given two points is:
Example. Find the equation of the line that passes through points (2, 5) and (-2, -3)
Solution: Let x1 = 2, y1 = 5, x2 = -2 and y2 = -3
The equation in slope intercept form is y = 2x + 1. The standard equation is -2x + y = 1.
C. Given the slope and a point
The formula in finding the equation of the line given the slope and a point is
y – y1 = m (x – x1)
Example. Find the equation of the line whose slope is –1 and passes through the point (5, -3)
Solution: y - (-3) = -1(x - 5)
y + 3 = -x + 5
y = -x - 2 or x + y = -2
D. Given the x - intercepts (a, 0) and the y-intercept (0, b)
The formula in finding the equation of the line given the intercepts is:
Example: The x and y intercepts of the line are –3 and 4 respectively. Find the equation of the line.
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LEARNING TASK
Find the equation of the line. Write in slope intercept form and in standard form
1. m = -5, b = 1
3. ( -2, 0) and (0, 5)
2. (1, -2), (3, 3)
4. a = 2, b = -7
5. m = 2, (3, -1)
1ST LONG QUIZ
I. MULTIPLE CHOICE: Choose the letter of the correct answer. Write your answers on the space
provided for.
______1. What is the process of finding the factors of an expression which is the reverse process of
multiplication?
A. factoring B. special product C. rationalization D. continuous division
______2. What is the Greatest Common Factor of 24 and 54?
A. 1
B. 2
C. 3
D. 6
______3. What is the GCF of 20, 24, and 40?
A. 1
B. 4
C. 8
D. 20
2
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______4. What is the GCF of 𝑥 and 𝑥 ?
A. 𝑥2
B. 𝑥7
C. 𝑥11
D. 𝑥18
2
______5. All of the following are factors of 12x . Except one. What is it?
A. 12
B. 12x
C. 12x2
D. 12x3
4
______6. What is the GCF of the expression 4x + 6x?
A. 2
B. 2x
C. x
D. 2x4
2
______7. If one factor of 4x + 6 is 2, what is the other factor?
A. 2x + 3
B. 4x + 6
C. 2x + 6
D. 2x2 + 3
______8. If one factor of 6ab2 – 12a2b3 is 1 – 2ab, what is the other factor?
A. 6ab
B. 6a2b
C. 6ab2
D. 6a2b2
______9. Which of the following is a perfect square?
A. 12x4
B. 16x2y2
C. 25x5y6
D. 36x6y7
______10. Which of the following expressions has factors (2x - y) and (2x + y)?
A. 2x2 + y2
B. 2x2 - y2
C. 4x2 + y2
D. 4x2 - y2
______11. What is the result when you square a binomial?
A. binomial B. sum of two squares C. difference of two squares D. perfect square trinomial
______12. What is the complete factored form of 4𝑥2 + 16𝑥𝑦 + 16𝑦2?
A. (2𝑥 + 4𝑦)2
B. (2𝑥 + 4𝑦)(2𝑥 − 4𝑦)
C. (2𝑥 − 4𝑦)2
D. (2𝑥 − 4𝑦)(2𝑥 − 4𝑦)
______13. What are the two numbers whose sum is 1 and whose product is -12?
A. 3 and -4
B. -3 and 4
C. -3 and -4
D. 3 and 4
______14. What is the complete factored form of 2𝑥2 + 5𝑥 − 3?
A. (2𝑥 − 1) (𝑥 − 3)
B. (2𝑥 + 1) (𝑥 + 3)
C. (2𝑥 − 1) (𝑥 + 3)
D. (2𝑥 + 1) (𝑥 − 3)
______15. Which of the following is the expanded form of (𝑥 − 5)2?
A. 𝑥 2 − 25
B. 𝑥 2 − 5𝑥 − 25
C. 𝑥 2 − 10𝑥 + 25
D. 𝑥 2 − 10𝑥 − 25
II. FACTORING. Factor the following completely.
1. x2 – 25
3. 3x2 + 30x + 75
2. 2x2 –15x –8
4. x3 - 27
5. 5x3 – 5x2 –10x
III. PROBLEM SOLVING. Solve the following problems.
1. If the area of the rectangle is given by the polynomial 2x 2 - 7x - 15, what is the dimension of
the rectangle in terms of x?
2. The length of a rectangular lot is 6 less than thrice its width. If the area is 45 square cm, what
is the length and the width of the rectangle?
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