Questions: On the set of aves below, graph the equation 3y+2x=15. Explain why (-6,9) is a solution to the equation.

On the set of aves below, graph the equation 3y+2x=15. Explain why (-6,9) is a solution to the equation.
Transcript text: On the set of aves below, graph the equation $3 y+2 x=15$. Explain why $(-6,9)$ is a solution to the equation.
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Solution

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Solution Steps

Step 1: Rewrite the equation in slope-intercept form

The given equation is 3y + 2x = 15. To rewrite it in slope-intercept form (y = mx + b), we isolate y:

3y = -2x + 15 y = (-2/3)x + 5

Step 2: Graph the equation

The y-intercept is 5, so plot the point (0, 5). The slope is -2/3, which means that for every 3 units we move to the right along the x-axis, we move 2 units down along the y-axis. From the point (0,5), we can find another point on the line by moving 3 units to the right and 2 units down, which gives us the point (3, 3). Plot this point and draw a line through (0, 5) and (3, 3).

Step 3: Explain why (-6, 9) is a solution

A point is a solution to an equation if it lies on the graph of the equation. Substitute x = -6 and y = 9 into the original equation:

3(9) + 2(-6) = 27 - 12 = 15

Since the equation holds true, the point (-6, 9) is a solution to the equation 3y + 2x = 15.

Final Answer:

The graph of the equation y = (-2/3)x + 5 is a straight line passing through points (0, 5) and (3, 3). The point (-6, 9) is a solution to the equation because it satisfies the equation 3y + 2x = 15.

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