Question

Find the slope and Y-Intercept of the graph of each equation

11x + y = 6
9x - 6y = 8
12x - 18y = 15
5x + y = 13
y + 3 - 5/2x - 5

Answer 1

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

Explanation:

`\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}}`

To find the slope and y-intercept of each equation, rearrange each equation so that it is in slope-intercept form.

`\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}`

Therefore:

• Slope = -11
• y-intercept = 6

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`\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 $6$}: & (9x-8)/(6)&=(6y)/(6)\\&\textsf{Simplify}: & (3)/(2)x-(4)/(3)&=y\\&\textsf{Slope-intercept form}: & y&=(3)/(2)x-(4)/(3)\end{aligned}`

Therefore:

• Slope = 3/2
• y-intercept = -4/3

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`\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 $18$}: & (12x-15)/(18)&=(18y)/(18)\\&\textsf{Simplify}: & (2)/(3)x-(5)/(6)&=y\\&\textsf{Slope-intercept form}: & y &= (2)/(3)x-(5)/(6)\end{aligned}`

Therefore:

• Slope = 2/3
• y-intercept = -5/6

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`\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}`

Therefore:

• Slope = -5
• y-intercept = 13

--------------------------------------------------------------------------------------------

`\begin{aligned}&\textsf{Given equation}: & y+3&=(5)/(2)x-5\\&\textsf{Subtract $3$ from both sides}: & y+3-3&=(5)/(2)x-5-3\\&\textsf{Simplify}: & y&=(5)/(2)x-8\\&\textsf{Slope-intercept form}: & y&=(5)/(2)x-8\end{aligned}`

Therefore:

• Slope = 5/2
• y-intercept = -8