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y=3x-1 Which of the following is the graph of the given system of equations? Choose 1 answer: (A) (B) (C) (D)

y=3x−1y=3x-1\newlineWhich of the following is the graph of the given system of equations?\newlineChoose 11 answer:\newline(A)\newline(B)\newline(C)\newline(D)

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Full solution

Q. y=3x−1y=3x-1\newlineWhich of the following is the graph of the given system of equations?\newlineChoose 11 answer:\newline(A)\newline(B)\newline(C)\newline(D)
  1. Understand Equation: Understand the equation y=3x−1y = 3x - 1. This is a linear equation in slope-intercept form, where the slope (m)(m) is 33 and the y-intercept (b)(b) is −1-1.
  2. Plot Y-Intercept: Plot the y-intercept on the graph.\newlineThe y-intercept is the point where the line crosses the y-axis. For the equation y=3x−1y = 3x - 1, the y-intercept is at (0,−1)(0, -1). Place a point on the graph at (0,−1)(0, -1).
  3. Find Another Point: Use the slope to find another point.\newlineThe slope of 33 means that for every 11 unit increase in xx, yy increases by 33 units. Starting from the y-intercept (0,−1)(0, -1), move 11 unit to the right (increasing xx by 11) and 33 units up (increasing yy by 33). This gives us another point on the line, which is 1122. Plot this point on the graph.
  4. Draw Line: Draw the line through the points.\newlineUsing a straight edge, draw a line through the points (0,−1)(0, -1) and (1,2)(1, 2). This line represents the graph of the equation y=3x−1y = 3x - 1.
  5. Identify Correct Graph: Identify the correct graph among the options.\newlineThe correct graph will be a straight line that passes through the points (0,−1)(0, -1) and (1,2)(1, 2). Without the actual graphs labeled (A)(A), (B)(B), (C)(C), and (D)(D), we cannot visually confirm which graph corresponds to the equation. However, the description provided should match one of the options given.

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