Question

Find the equation of the line with slope -1 and that contains the point (-4, -3). Write the equation in the form y = mx + b and identify m and b. m = b =

Answer 1

The coordinate given is

`\begin{gathered} (-4,-3) \\ x_1=-4,y_1=-3 \end{gathered}`

The slope given is

`m=-1`

The general equation of a line is given below as

`\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

Concept:

The formula to calculate the equation of a line when one slope and one point is given is

`m=(y-y_1)/(x-x_1)`

Step 1:

Substitute the values in the formula above

`\begin{gathered} m=(y-y_1)/(x-x_1) \\ -1=(y-(-3))/(x-(-4)) \\ -1=(y+3)/(x+4) \end{gathered}`

Step 2:

Cross multiply the equation above

`\begin{gathered} -1=(y+3)/(x+4) \\ y+3=-1(x+4) \\ y+3=-x-4 \\ \text{substract 3 from both sides} \\ y+3-3=-x-4-3 \\ y=-x-7 \end{gathered}`

Hence,

The equation of the line is y = -x -7

where the slope is m = -1

the y-intercept is b = -7