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Graph
-27 x+18 y=54.

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

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Solve one-step equations with whole numbers

Full solution

Q. Graph

-27x+18y=54

.

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: $\newline$ $-27x + 18y + 27x = 54 + 27x$ $\newline$ This simplifies to: $\newline$ $18y = 27x + 54$
Solving for y: Next, we divide every term by $18$ to solve for y: $\newline$ $(\frac{18y}{18}) = (\frac{27x}{18}) + \frac{54}{18}$ $\newline$ This simplifies to: $\newline$ $y = (\frac{3}{2})x + 3$
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 $\frac{3}{2}$ , 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 $y = \frac{3}{2}x + 3$ .

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