This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Answer Question 7. The graph of a linear equation is a straight line. Answer: straight line Step 2: Answer Question 8 by identifying the intercepts from the graph. The x-intercept is the point where the line crosses the x-axis (where y=0). From the graph, the line crosses the x-axis at x = -2. The y-intercept is the point where the line crosses the y-axis (where x=0). From the graph, the line crosses the y-axis at y = -1. Answer: x-intercept: (-2, 0), y-intercept: (0, -1) Step 3: Answer Question 9 by finding the inequalities for the shaded region. The shaded region is bounded by the x-axis (y=0), the y-axis (x=0), and a diagonal line. The diagonal line passes through (0, 12) and (6, 0). First, find the slope of the line: m = (y_2 - y_1)/(x_2 - x_1) = (0 - 12)/(6 - 0) = (-12)/(6) = -2 Next, use the point-slope form y - y_1 = m(x - x_1) with point (6, 0): y - 0 = -2(x - 6) y = -2x + 12 Rearrange to standard form: 2x + y = 12 The shaded region is below this line. Test a point in the shaded region, e.g., (1, 1): 2(1) + 1 = 3 Since 3 < 12, the inequality is 2x + y 12. The region is also to the right of the y-axis, so x 0. The region is also above the x-axis, so y 0. Answer: 2x + y 12, x 0, y 0 Step 4: Answer Question 10 by setting up and solving an equation. Let the first integer be n. The next consecutive integer is n+1. The sum of these two integers is 47. n + (n+1) = 47 2n + 1 = 47 Subtract 1 from both sides: 2n = 47 - 1 2n = 46 Divide by 2: n = (46)/(2) n = 23 The first integer is 23. The second integer is n+1 = 23+1 = 24. Answer: The integers are 23 and 24. Send me the next one 📸