Exercise 1 Page 86

Equations in slope-intercept form follow a certain format. In this form, $m$ is the slope and $b$ is the $y\text{-}$intercept. The line has a slope of $\text{-}3$ which means that we can substitute $m=\text{-}3.$

$$\begin{array}{c}y=\text{-}3x+b\end{array}$$

To write a complete equation for this line, we also need to determine the $y\text{-}$intercept $b.$ We can do that by substituting the given point $(1,\text{-}4)$ into the equation and solving for $b.$

$y=\text{-}3x+b$

SubstituteII

$x=1$, $y=\text{-}4$

$\text{-}4=\text{-}3(1)+b$

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Solve for $b$

Multiply

Multiply

$\text{-}4=\text{-}3+b$

AddEqn

$\text{LHS}+3=\text{RHS}+3$

$\text{-}1=b$

RearrangeEqn

Rearrange equation

$b=\text{-}1$

Now that we have both the slope and the $y\text{-}$intercept, we can write the final equation.

$$\begin{array}{c}y=\text{-}3x+(\text{-}1)\iff y=\text{-}3x-1\end{array}$$