Question

Write the equation of the line in slope intercept form that is parallel to the given line and goes through the given point.y=3×+1; (-3,-2)

Answer 1

`y=3x+7`

Step-by-step explanation

Step 1

remember the slope intercep form

`y=mx+b`

where m is the slope, and b is the y-intercept

so, we have

`y=3x+1\rightarrow y=mx+b`

hence,for the given line

slope=3

b=1

Step 2

2 lines are parallel if the slope is the same, so the slope of the line we are looking for is 3 too.

`\begin{gathered} \text{if line 1}\parallel Line2 \\ \text{then} \\ \text{slope}_1=slope_2 \end{gathered}`

therefore, we need a line that has

slope=3

and passes through (-3,-2)

we can use

`\begin{gathered} y-y_1=slope(x-x_1) \\ \text{where} \\ \text{the point is(x}_(1,)y_1) \end{gathered}`

replace

`\begin{gathered} y-y_1=slope(x-x_1) \\ y-(-2)=3(x-(-3)) \\ y+2=3(x+3) \\ y+2=3x+9 \\ \text{subtract 2 in both sides} \\ y+2-2=3x+9-2 \\ y=3x+7 \end{gathered}`

I hope this helps you