Answer:
1) Slope = -11, y-intercept = 6
2) Slope = 3/2, y-intercept = -4/3
3) Slope = 2/3, y-intercept = -5/6
4) Slope = -5, y-intercept = 13
5) Slope = 5/2, y-intercept = -8
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
To find the slope and y-intercept of each equation, rearrange each equation so that it is in slope-intercept form.
[tex]\begin{aligned}&\textsf{Given equation}: & 11x + y & = 6\\&\textsf{Subtract $11x$ from both sides}: \quad & 11x + y-11x & = 6-11x\\&\textsf{Simplify}: & y & = 6-11x\\&\textsf{Slope-intercept form}: & y&=-11x+6\end{aligned}[/tex]
Therefore:
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[tex]\begin{aligned}&\textsf{Given equation}: & 9x-6y&=8\\&\textsf{Add $6y$ to both sides}: \quad & 9x-6y+6y&=8+6y\\&\textsf{Simplify}: & 9x&=8+6y\\&\textsf{Subtract $8$ from both sides}: & 9x-8&=8+6y-8\\&\textsf{Simplify}: & 9x-8&=6y\\&\textsf{Divide both sides by $6$}: & \dfrac{9x-8}{6}&=\dfrac{6y}{6}\\&\textsf{Simplify}: & \dfrac{3}{2}x-\dfrac{4}{3}&=y\\&\textsf{Slope-intercept form}: & y&=\dfrac{3}{2}x-\dfrac{4}{3}\end{aligned}[/tex]
Therefore:
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[tex]\begin{aligned}&\textsf{Given equation}: & 12x - 18y &= 15\\&\textsf{Add $18y$ to both sides}: \quad & 12x - 18y +18y&= 15+18y\\&\textsf{Simplify}: & 12x&=15+18y\\&\textsf{Subtract $15$ from both sides}: & 12x-15&=15+18y-15\\&\textsf{Simplify}: & 12x-15&=18y\\&\textsf{Divide both sides by $18$}: & \dfrac{12x-15}{18}&=\dfrac{18y}{18}\\&\textsf{Simplify}: & \dfrac{2}{3}x-\dfrac{5}{6}&=y\\&\textsf{Slope-intercept form}: & y &= \dfrac{2}{3}x-\dfrac{5}{6}\end{aligned}[/tex]
Therefore:
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[tex]\begin{aligned}&\textsf{Given equation}: & 5x + y &= 13\\&\textsf{Subtract $5x$ from both sides}: \quad & 5x + y-5x &= 13-5x\\&\textsf{Simplify}: & y&=13-5x\\&\textsf{Slope-intercept form}: & y&=-5x+13\end{aligned}[/tex]
Therefore:
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[tex]\begin{aligned}&\textsf{Given equation}: & y+3&=\dfrac{5}{2}x-5\\&\textsf{Subtract $3$ from both sides}: & y+3-3&=\dfrac{5}{2}x-5-3\\&\textsf{Simplify}: & y&=\dfrac{5}{2}x-8\\&\textsf{Slope-intercept form}: & y&=\dfrac{5}{2}x-8\end{aligned}[/tex]
Therefore:
