Question

write the slope - intercept form of the equation of the line slope. 7) through: (4, -1), slope = 1

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m = 1$ and the line passes through the point $(x,y)=(4,-1)$.

Step2: Substitute values into the equation

Substitute $x = 4$, $y=-1$ and $m = 1$ into $y=mx + b$:
\[

$$\begin{align*} -1&=(1)\times(4)+b\\ -1&=4 + b \end{align*}$$

\]

Step3: Solve for $b$

Subtract 4 from both sides of the equation $-1=4 + b$:
\[

$$\begin{align*} b&=-1-4\\ b&=-5 \end{align*}$$

\]

Step4: Write the equation

Now that we know $m = 1$ and $b=-5$, substitute these values back into the slope - intercept form $y=mx + b$:
\[y=x-5\]

Answer:

$y = x-5$