# Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises - Page 113: 44

$y=-\dfrac{2}{3}x +6$

#### Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b = y-intercept. (2) Parallel lines have equal slopes. Transform $2x+3y+4=0$ to slope-intercept form to obtain: $2x+3y+4=0 \\3y=-2x-4 \\\dfrac{3y}{3}=\dfrac{-2x-4}{3} \\y = -\dfrac{2}{3}x -\dfrac{4}{3}$ The slope of this line is $-\dfrac{2}{3}$. The line we are looking for the equation of is parallel to the line above. Thus, the slope of the line is also $-\dfrac{2}{3}$. This means that a tentative equation of the line is: $y=-\dfrac{2}{3}x+b$ The y-intercept of the line we are looking for is $6$. This means that $b=6$. Therefore, the equation of the line we are looking for is: $y=-\dfrac{2}{3}x +6$

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