Chapter 2 - Section 2.3 - Lines - 2.3 Assess Your Understanding - Page 179: 82

$\text{slope}=m=-\frac{3}{2}; \\\text{y-intercept}=b=3$

Work Step by Step

RECALL: The slope-intercept form of a line's equation is: $y=mx+b$ where $m$ = slope and $b$ = y-intercept Write the given equation in slope-intercept form by isolating $y$ on one side to obtain: $3x+2y=6 \\2y = -3x+6 \\y=\frac{-3x+6}{2} \\y = -\frac{3}{2}x+3$ The equation above has: $\text{slope}=m=-\frac{3}{2}; \\\text{y-intercept}=b=3$ To graph the line, perform the following steps: (1) Plot the y-intercept point $(0, 3)$. (2) Use the slope $-\frac{3}{2}$ to find another point on the line. From $(0, 3)$, move down 3 units (the rise) and move 2 units to the right (the run) to arrive at the point $(2, 0)$. (3) Complete the graph by connecting the two points using a straight line. (refer to the attached image in the answer part above for the graph)

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