Slope-of-a-line-given-equation (1).docx

Slope of a Line Given Equation -In many instances, the linear equations are usually written in standard form Ax + By=C Wherein, A, B, and C are real numbers and A≠0. Finding the slope of a line given equation, however, requires the use of other forms depending on the given properties of the equation. -We should change the linear equations from standard form (Ax + By=C) to Slope-Intercept form y=mx + b Wherein, y has a slope m and y-intercept b.

2. Changing Standard Form to Slope-Intercept Form In order to go from one form to another, all you have to do is change the order of the given numbers. First you want to move the Ax to the opposite side of the equation, by either adding or subtracting it. At this point your equation will be set up By = -Ax + C. Then you want to divide the B from the By and the rest of the equation. Therefore you will have y = - Ax/B + C/B. This is the same thing as the slope-intercept form, just a few of the letters are different.

Examples: a. A=4 B=2 C=10 4x+2y=10 2y= -4x+10

1. Formula for Standard Form: −𝐴 𝐵 Example: a. A= 4 B=2 C=10 4x+2y=10 −4 2

÷2

Therefore, slope is -2

y= -2x+5 Therefore, slope is -2 b. A=3 B= -1 C= 1 3x-y=1 -y=-3x+1 y=3x-1 Therefore, slope is 3 Now that you’ve finally understood the lesson, let’s test your skills with these MATHinik exercises.

MATHinik Exercises II.

I.

Choose the letter of the correct answer in the questions below. 1. -6x + 2y=4 a. 3 b. -2 c. -3 d. 2

Find the slope of the given equation:

6. 6x + 3y=2

2. 8x + 4y=16

7. 3x + 2y=5 a. -4 b. -3 c. -2 d. -1 8. x + 2y= -3

3. -18x + 3y=21 a. 9 b. 6 c. 3 d. -3 9. 5x + 9y=7 4. 12x – 4y= 24 a. 1 b. 2 c. 3 d. -1

10. -3x + 2y= -6

5. 2x – y=10 a. -2 b. -1 c. 1 d. 2 Math FYI Writing equations has been in existence since 4500 years ago, in early civilization of Babylon, Egypt, and Greece. However, equations were written using little pictures to represent unknowns. It was only when Diophantus, a Greek mathematician, introduced the algebraic symbolism. The syncopated style of writing equations gained wide acceptance

Direction: Find the slope in each given equation. Have fun!

Test Yourself: Puzzle Mania

8x-2y=1

16x-3y=24

6x + 5y= -14

3x + 5y=9

3x-7y= -15

5x-2y=10

5x + 15y=3

5x-3y=18

7x + 2y=14

4x-8y=3

24x-6y=12

-3x-18y=15

2x-4y=4

-2x + 3y=6

-3x-9y=12

2x-y=4

-14x + 6y=8

42x – 24y = 84

Math

Challenge

What is the slope in 𝒙 𝒚 the equation + =

What is the slope in 𝒙 𝒚 the equation + =

1?

1?

𝟑

𝟓

𝟑

𝟓

Math FYI It was probably due to René Descartes (1596-1950), a French mathematician and philosopher, that equations received a closer look. His development of the coordinate system paved the way to analytic study of lines, its properties and applications. History rewarded Descartes’ contribution by giving him the title “Father of Analytic Geometry” and named his inventions after him – the Cartesian coordinate system.