University:
California State University, Northridge
Course:
MATH 351 | Differential Equations
Academic year:

2024
Views:

450

Pages:

2
Author:

Javon Neal

Question 1 Find slope and y-intercept of 𝑦 = 6 y=6. Answer 1 Firstly, graph 𝑦 = 6 y=6. The line crosses the y-axis at 6, as the line is always at that value. As it is a horizontal line, the slope is 0. Answer 2 The equation 𝑦 = 6 y=6 means for each and every value of 𝑥 x, 𝑦 y will be equal to 6. This is the definition of a horizontal line. Thus, by definition, the slope of a horizontal line is 0. Question 2 How do you graph the equation 𝑦 = 𝑥 y=x? Answer 1 We can rewrite 𝑦 = 𝑥 y=x into a general form of slope-intercept equation: 𝑦 = 𝑚 𝑥 + 𝑏 , with 𝑚 = 1 , 𝑏 = 0 y=mx+b, with m=1,b=0 𝑦 = 1 𝑥 + 0 y=1x+0 And we have: slope = rise run = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 slope= run rise = x 2 −x 1 y 2 −y 1 Answer 2 We can also see that for every value we choose of 𝑥 x, we will get the exact same value for 𝑦 y and can therefore plot points such as ( 0 , 0 ) , ( 2 , 2 ) , ( − 3 , − 3 ) (0,0),(2,2),(−3,−3). Question 3 Write some examples of inverse operations, please. Answer 1 Examples of inverse operations: Addition and subtraction; Multiplication and division; Squares and square roots. Answer 2 For example, subtraction and addition, multiplication and division. Question 4 How to graph 𝑥 = 6 x=6 by plotting points? Answer 1 𝑥 x will always be 6. You end up with a parallel line, where 𝑥 x-intercept is 6, as says the equation. Answer 2 You get a line parallel to the y-axis and 𝑥 x-intercept which is 6. Question 5 How to graph 𝑥 = − 3 x=−3? Answer 1 It’s the equation of a vertical line passing through 𝑥 = − 3 x=−3. Answer 2 𝑥 = − 3 x=−3 is a graph that is a vertical line with all the 𝑥 x-coordinates equal to -3.