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

2024
Views:

207

Pages:

3
Author:

Javon Neal

Question 1 We give linear equations. For each equation, a. Find the y-intercept and slope. b. Determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. Use two points to graph the equation. 𝑦 = − 3 y=−3 Answer a. The y-intercept is the constant in the linear equation: − 3 −3 The slope is the coefficient of 𝑥 x in the linear equation: 0 0 b. If the slope is positive, then the graph slopes upwards. If the slope is negative, then the graph slopes downwards. If the slope is 0 0, then the graph is horizontal. Slope = 0 → Horizontal Slope =0→Horizontal c. Evaluate the given equation for two values of 𝑥 x. Graph the two points. Draw a line through the two points: (Graph displayed showing points ( 0 , − 3 ) (0,−3) and ( 1 , − 3 ) (1,−3) forming a horizontal line.) Results: a. − 3 −3 b. Horizontal c. See graph Question 2 Graph linear and Y intercepts 𝑌 = 4 𝑥 − 2 Y=4x−2. Answer 𝑥 = 0 , so 𝑦 = − 2 , point: ( 0 , − 2 ) x=0, so y=−2, point: (0,−2) 𝑥 = 5 , so 𝑦 = 20 − 2 = 18 , so point: ( 5 , 18 ) x=5, so y=20−2=18, so point: (5,18) Question 3 A system of linear equations is a set of two or more equations taken together. The point where the two graphs intersect is called the solution. 𝑦 = 1 3 𝑥 − 3 y= 3 1 x−3 𝑦 = − 𝑥 + 1 y=−x+1 a) Complete the table for each linear function. 𝑥 x 𝑦 = 1 3 𝑥 − 3 y= 3 1 x−3 ( 𝑥 , 𝑦 ) (x,y) -6 -5 (-6, -5) -3 -4 (-3, -4) 0 -3 (0, -3) 3 -2 (3, -2) 6 -1 (6, -1) 𝑥 x 𝑦 = − 𝑥 + 1 y=−x+1 ( 𝑥 , 𝑦 ) (x,y) -2 3 (-2, 3) -1 2 (-1, 2) 0 1 (0, 1) 1 0 (1, 0) 2 -1 (2, -1) b) Graph both equations on the coordinate plane below. Answer a) (Graph displayed with both linear equations plotted. Intersection point at ( − 2 , 3 ) (−2,3). Solution = ( − 2 , 3 ) (−2,3).) b) Graph for the above table is provided.