Given the linear equations below: a) y = 3x + 1 b) y = -2x + 2 a. From the equations, derive the value of the gradient and y-intercept. b. Plot the graph of on a common axis. c. Is the function increasing, decreasing or constant?

Here are the solutions for the given linear equations: For equation a) y = 3x + 1 Step 1: Identify the gradient and y-intercept. The equation is in the form y = mx + c, where m is the gradient and c is the y-intercept. Comparing y = 3x + 1 with y = mx + c: • The gradient m is the coefficient of x. • The y-intercept c is the constant term. m = 3 c = 1 The y-intercept is the point (0, c), which is (0, 1). Step 2: Provide points for plotting the graph. To plot the graph, we need at least two points. We already have the y-intercept (0, 1). Let's find another point by choosing an x-value, for example, x=1. When x = 1: y = 3(1) + 1 y = 3 + 1 y = 4 So, another point is (1, 4). To plot the graph, draw a Cartesian plane, mark the points (0, 1) and (1, 4), and draw a straight line passing through them. Step 3: Determine if the function is increasing, decreasing, or constant. The nature of the function is determined by the sign of the gradient. • If m > 0, the function is increasing. • If m < 0, the function is decreasing. • If m = 0, the function is constant. Since the gradient m = 3, which is greater than 0, the function is increasing. For equation b) y = -2x + 2 Step 1: Identify the gradient and y-intercept. Comparing y = -2x + 2 with y = mx + c: • The gradient m is the coefficient of x. • The y-intercept c is the constant term. m = -2 c = 2 The y-intercept is the point (0, c), which is (0, 2). Step 2: Provide points for plotting the graph. We have the y-intercept (0, 2). Let's find another point by choosing an x-value, for example, x=1. When x = 1: y = -2(1) + 2 y = -2 + 2 y = 0 So, another point is (1, 0). To plot the graph, draw a Cartesian plane, mark the points (0, 2) and (1, 0), and draw a straight line passing through them. Step 3: Determine if the function is increasing, decreasing, or constant. Since the gradient m = -2, which is less than 0, the function is decreasing. Here's a summary of the answers: 1. From the equations above, state the value of: a) the gradient and y-intercept For y = 3x + 1: Gradient: 3 Y-intercept: 1 For y = -2x + 2: Gradient: -2 Y-intercept: 2 b) Plot the graph of each equation on a Cartesian plane. For y = 3x + 1: Points for plotting: (0, 1) and (1, 4) For y = -2x + 2: Points for plotting: (0, 2) and (1, 0) c) Is the function increasing, decreasing or constant? For y = 3x + 1: The function is increasing. For y = -2x + 2: The function is decreasing. Drop the next question! 📸