Writing the equation in slope-intercept form: To graph the equation −27x+18y=54, we first need to write it in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
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 27x to both sides of the equation:−27x+18y+27x=54+27xThis simplifies to:18y=27x+54
Solving for y: Next, we divide every term by 18 to solve for y:(1818y)=(1827x)+1854This simplifies to:y=(23)x+3
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 m is 23, and the y-intercept b is 3.
Plotting the y-intercept: To graph the equation, we start by plotting the y-intercept (0,3) on the y-axis.
Finding another point using the slope: Next, we use the slope to find another point. Starting from the y-intercept, we move 3 units up (since the slope is positive) and 2 units to the right (the denominator of the slope). This gives us a second point on the graph.
Drawing the graph: With two points plotted, we can draw a straight line through them to represent the graph of the equation y=23x+3.
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