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Graph 
-27 x+18 y=54.

Graph 27x+18y=54-27x+18y=54.

Full solution

Q. Graph 27x+18y=54-27x+18y=54.
  1. Writing the equation in slope-intercept form: To graph the equation 27x+18y=54-27x + 18y = 54, we first need to write it in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  2. Isolating y on one side of the equation: We can start by isolating y on one side of the equation. To do this, we can add 27x27x to both sides of the equation:\newline27x+18y+27x=54+27x-27x + 18y + 27x = 54 + 27x\newlineThis simplifies to:\newline18y=27x+5418y = 27x + 54
  3. Solving for y: Next, we divide every term by 1818 to solve for y:\newline(18y18)=(27x18)+5418(\frac{18y}{18}) = (\frac{27x}{18}) + \frac{54}{18}\newlineThis simplifies to:\newliney=(32)x+3y = (\frac{3}{2})x + 3
  4. Identifying the slope and y-intercept: Now that we have the equation in slope-intercept form, we can identify the slope and y-intercept. The slope mm is 32\frac{3}{2}, and the y-intercept bb is 33.
  5. Plotting the y-intercept: To graph the equation, we start by plotting the y-intercept (0,3)(0,3) on the y-axis.
  6. Finding another point using the slope: Next, we use the slope to find another point. Starting from the yy-intercept, we move 33 units up (since the slope is positive) and 22 units to the right (the denominator of the slope). This gives us a second point on the graph.
  7. Drawing the graph: With two points plotted, we can draw a straight line through them to represent the graph of the equation y=32x+3y = \frac{3}{2}x + 3.