Question

y=-x-5A line has the equationFind the equation of a parallel7. line passing through (3,2).

Answer 1

slope

Explanation

Step 1

Fin the slope of the line:

the function

$y=-x-5$

is written in the slope-intercept form:

$\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}$

therefore, we can conclude

$\begin{gathered} y=mx+b\rightarrow y=-x-5 \\ \text{slope}_1=m=-1 \end{gathered}$

the solpe1 is -1

Now, we know that 2 lines are parallel if they have the same slope,

so

$\begin{gathered} \text{ line 1 }\parallel\text{ line 2} \\ \text{then} \\ \text{slope}1=\text{slope}2 \\ -1=\text{slope}2 \end{gathered}$

it means the slope of the line we are looking for is -1

Step 2

now, we have the slope and a point of the line, we can use

$\begin{gathered} y-y_0=m(x-x_0) \\ \text{where m is the slope and } \\ (x_0,y_o)\text{ is a point of the line} \end{gathered}$

then, let's replace

let P(3,2)

$\begin{gathered} y-y_0=m(x-x_0) \\ y-2=-1(x-3) \\ y-2=-x+3 \\ \text{add 2 in both sides} \\ y-2+2=-x+3+2 \\ y=-x+5 \end{gathered}$

therefore, the equation is

$y=-x+5$

I hope this helps you