The graphs of the equations are:
In fig. 1:
a) y = x (red line)
b) y = -x (blue line)
c) y = x + 5 (green line)
In Fig. 2:
a. y = 3x + 2 (red line)
b. y = 3x - 2 (blue line)
<h3>What is the Graph of a Linear Equation?</h3>A linear equation can be expressed in slope-intercept form as, y = mx + b, where m is the slope of the line and b is the y-intercept where the line cuts across the vertical axis (y-axis).
Given the equations:
a) y = x, the slope is 1, while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the red line on the graph plotted).
b) y= -x, the slope is -1 (declining slope), while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the blue line on the graph plotted).
c) y = x + 5, the slope is 1 (rising slope), while the y-intercept is 5. This means the line of the graph passes the y-axis at 5. (It is the green line on the graph plotted).
In Figure 2, we have the second graph with the following equations:
a. y = 3x + 2, the slope is 3 (rising slope), while the y-intercept is 2. This means the line of the graph passes the y-axis at 2. (It is the red line on the graph plotted).
b. y = 3x - 2, the slope is 3 (rising slope), while the y-intercept is -2. This means the line of the graph passes the y-axis at -2. (It is the blue line on the graph plotted).
In summary, the graphs of the equations are:
In fig. 1:
a) y = x (red line)
b) y = -x (blue line)
c) y = x + 5 (green line)
In Fig. 2:
a. y = 3x + 2 (red line)
b. y = 3x - 2 (blue line)
Learn more about the graph of a linear equation on:
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