Solve the following system of equations graphically on the set of axes below.
y = -1/4x + 4
5x – 4y = 8
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 = -1/4x + 4 5x – 4y = 8 Plot two lines by clicking the graph. Click a line to delete it.
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To solve the system of equations graphically, follow these steps:
1. Convert the second equation to slope-intercept form (y = mx + b):
The second equation is:
[ 5x – 4y = 8 ]
Rearranging it to solve for ( y ), we get:
[ -4y = -5x + 8 ]
[ y = frac{5}{4}x – 2 ]
2. Identify the two equations:
You now have:
– First equation: ( y = -frac{1}{4}x + 4 )
– Second equation: ( y = frac{5}{4}x – 2 )
3. Graph the equations:
– For the first equation (( y = -frac{1}{4}x + 4 )), the y-intercept is 4. The slope is -1/4, meaning for every 4 units you move right, go down 1 unit.
– For the second equation (( y = frac{5}{4}x – 2 )), the y-intercept is -2. The slope is 5/4, meaning for every 4 units you move right, go up 5 units.
4. Find the intersection point:
Plot both lines on the same axes and look for the point