Question 7 - End-of-Chapter Exercises - Chapter 2 Class 9 - Introduction to Linear Polynomials (Ganita Manjari

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Question 7 (i) Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates of the points where these lines cut the y-axis. (i) y = –3x + 4 Let’s find points which lie on the line Putting x = 0 y = –3 × 0 + 4 y = 0 + 4 y = 4 So, x = 0, y = 4 lie on the line i.e. (0, 4) lies on the line Putting x = 1 y = –3 × 1 + 4 y = –3 + 4 y = 1 So, x = 1, y = 1 lie on the line i.e. (1, 1) lies on the line y = –3x + 4 Thus, for line y = –3x + 4 Slope: –3 y-intercept: 4 Cuts y-axis at: (0, 4) Question 7 (ii) Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates of the points where these lines cut the y-axis. (ii) 2y = 4x + 7 Let’s find points which lie on the line Putting x = 0 2y = 4 × 0 + 7 2y = 0 + 7 2y = 7 y = 7/2 = 3.5 So, x = 0, y = 3.5 lie on the line i.e. (0, 3.5) lies on the line Putting x = 1 2y = 4 × 1 + 7 2y = 4 + 7 2y = 11 y = 11/2 = 5.5 So, x = 0, y = 5.5 lie on the line i.e. (0, 5.5) lies on the line 2y = 4x + 7 Thus, for line 2y = 4x + 7 Dividing by 2 both sides (so that number multiplied by y becomes 1) 2𝑦/2 = 4𝑥/2 + 7/2 y = 2x + 𝟕/𝟐 So, we can write Slope: 2 y-intercept: 𝟕/𝟐 Cuts y-axis at: (0, 𝟕/𝟐) Question 7 (iii) Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates of the points where these lines cut the y-axis. (iii) 5y = 6x – 10 Let’s find points which lie on the line Putting x = 0 5y = 6 × 0 – 10 5y = 0 – 10 5y = –10 y = (−10)/5 = –2 So, x = 0, y = –2 lie on the line i.e. (0, –2) lies on the line Putting x = 5 5y = 6 × 5 – 10 5y = 30 – 10 5y = 20 y = 20/5 = 4 So, x = 0, y = 4 lie on the line i.e. (0, 4) lies on the line 5y = 6x – 10 Thus, for line 5y = 6x – 10 Dividing by 5 both sides (so that number multiplied by y becomes 1) 5𝑦/5 = 6𝑥/5 – 10/5 y = 𝟔𝒙/𝟓 – 2 So, we can write Slope: 𝟔/𝟓 y-intercept: –2 Cuts y-axis at: (0, –2) Question 7 (iv) Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates of the points where these lines cut the y-axis. (iv) 3y = 6x – 11 Let’s find points which lie on the line Putting x = 0 3y = 6 × 0 – 11 3y = 0– 11 3y = –11 y = (−11)/3 = –3.66 So, x = 0, y = –3.66 lie on the line i.e. (0, –3.66) lies on the line Putting x = 2 3y = 6 × 2 – 11 3y = 12 – 11 3y = 1 y = 1/3 = 0.33 So, x = 2, y = 0.33 lie on the line i.e. (0, 0.33) lies on the line 3y = 6x – 11 Thus, for line 3y = 6x – 11 Dividing by 3 both sides (so that number multiplied by y becomes 1) 3𝑦/3 = 6𝑥/3 – 11/3 y = 2x – 𝟏𝟏/𝟑 So, we can write Slope: 2 y-intercept: 𝟏𝟏/𝟑 Cuts y-axis at: (0, 𝟏𝟏/𝟑) Also, we are asked if any of the lines are parallel (i) y = –3x + 4 (ii) 2y = 4x + 7 (iii) 5y = 6x – 10 (iv) 3y = 6x – 11 Parallel lines have the exact same slope. Here, equations (ii) and (iv) both have a slope of 2, so they are parallel.