Solve the following system of equations graphically on the set of axes below.
y = 1/2 x + 7
3x + y = -7
Plot two lines by clicking the graph.
Click a line to delete it.
Solve the following system of equations graphically on the set of axes below. y = 1/2 x + 7 3x + y = -7 Plot two lines by clicking the graph. Click a line to delete it
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To solve the system of equations graphically, we’ll start by rewriting each equation in slope-intercept form (y = mx + b) and then plot the lines.
1. Equation 1:
( y = frac{1}{2}x + 7 )
– The slope (m) is ( frac{1}{2} ), and the y-intercept (b) is 7. You can start plotting this line by marking the point (0, 7) on the y-axis and then using the slope to find another point. For instance, from (0, 7), move right 2 units (x increases by 2) and up 1 unit (y increases by 1) to get to the point (2, 8).
2. Equation 2:
Rearranging ( 3x + y = -7 ) into slope-intercept form gives:
( y = -3x – 7 )
– The slope here is -3, and the y-intercept is -7. Start by marking (0, -7) on the y-axis. From this point, for every 1 unit you move to the right (2 increase in x), move down 3 units to plot additional points. For example, moving to (1, -10).
Now, plot these two lines on your graph. The solution to the system of equations is where