Answer no 1on a graph

Mathematics

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Graph of y = 2x + 5

Use the left and right arrow keys to trace the curve, up and down to jump between key points, and plus and minus to zoom.

Key points of y = 2x + 5
Pointxy
x-intercept−2.50
y-intercept05

Step-by-step solution

2 steps
  1. Prepare the table of values for y=2x+5y = 2x + 5.

    To draw the graph, first calculate the yy values for xx ranging from −3-3 to 4.

    xx2x2x+5+5y=2x+5y = 2x + 5(x,y)(x, y)
    −3-3−6-6+5+5−1-1(−3,−1)(-3, -1)
    −2-2−4-4+5+51(−2,1)(-2, 1)
    −1-1−2-2+5+53(−1,3)(-1, 3)
    00+5+55(0,5)(0, 5)
    12+5+57(1,7)(1, 7)
    24+5+59(2,9)(2, 9)
    36+5+511(3,11)(3, 11)
    48+5+513(4,13)(4, 13)
  2. Plot the graph using the given scale.

    • Draw a horizontal xx-axis and a vertical yy-axis on graph paper.
    • Mark the origin (0,0)(0,0) where the axes intersect.
    • Apply the scale: 2 cm2 \text{ cm} represents 1 unit1 \text{ unit} on both axes. This means that every 2 cm2 \text{ cm} grid line (or every large square) should be labeled as 1,2,3,…1, 2, 3, \dots for positive values and −1,−2,−3,…-1, -2, -3, \dots for negative values on both axes.
    • Plot each point from the table above on your graph paper. For example, for (−3,−1)(-3, -1), move 3 units left on the xx-axis and 1 unit down on the yy-axis.
    • Once all points are plotted, use a ruler to draw a straight line that passes through all these points. Extend the line to the edges of your graph paper.
    • Label the line with its equation: y=2x+5y = 2x + 5.

    This process will create the graph of the linear equation.

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