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Sagot :
First let's put the equation 4y + 9 = 2x in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. So we have that:
[tex]\begin{gathered} 4y+9=2x \\ 4y=2x-9 \\ y=\frac{2x-9}{4} \\ y=\frac{1}{2}x-\frac{9}{4} \end{gathered}[/tex]The slope of this equation is 1/2. In order to the second line be parallel to this line, it has to have the same slope. Also, since the second line passes through the point (7, 2), we have:
[tex]\begin{gathered} y=\frac{1}{2}x+b \\ (7,2)\colon \\ 2=\frac{1}{2}\cdot7+b \\ 2=\frac{7}{2}+b \\ b=2-\frac{7}{2}=\frac{4-7}{2}=-\frac{3}{2} \end{gathered}[/tex]So the second equation is:
[tex]y=\frac{1}{2}x-\frac{3}{2}[/tex]
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