Part each equation in slope-intercept form and graph. Clearly mark at least three points on each line
2x + 6y = 18
To rewrite the equation in slope-intercept form, we need to solve for y:
2x + 6y = 18
Subtract 2x from both sides:
6y = -2x + 18
Divide both sides by 6:
y = (-2/6)x + 3
Simplifying the equation gives us the equation in slope-intercept form, y = (-1/3)x + 3.
Now we will graph the equation:
To find the three points on the line, we can assign values to x and solve for y. Let's choose three values for x:
When x = 0:
y = (-1/3)(0) + 3 = 3
So one point is (0, 3).
When x = 3:
y = (-1/3)(3) + 3 = 2
So another point is (3, 2).
When x = 6:
y = (-1/3)(6) + 3 = 1
So another point is (6, 1).
Plotting these points on the graph gives us:
(-1/3) | .
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0 3 6 9
The graph is a straight line that passes through the points (0, 3), (3, 2), and (6, 1).