Question

Try it

Use the graph and table to write the equation that
describes the line graphed.
5
y
X
4.
1
3
-2
N
2
2
-1
الم
3
0
3
4
5
4
-5
-3 2-1
- 1
5
-2
2
-3
4
The equation of the line is
y = x + 1
y=-x+1
y = -x +3
y = x + 3
Done

Answer 1

Given:

Find-:

Equation of a line.

Sol:

General equation of a line.

`y=mx+c`

Where,

`\begin{gathered} m=\text{ slope} \\ \\ m=(x_2-x_1)/(y_2-y_1) \\ \\ c=\text{ y-intercept.} \end{gathered}`

Choose any two-point then:

`\begin{gathered} (-2,1)=(x_1,y_1) \\ \\ (-1,2)=(x_2,y_2) \end{gathered}`

So the slope of the line is:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ m=(2-1)/(-1-(-2)) \\ \\ m=(1)/(-1+2) \\ \\ m=1 \end{gathered}`

So the equation become:

`\begin{gathered} y=mx+c \\ \\ y=(1)x+c \\ \\ y=x+c \end{gathered}`

So y-intercept is:

`\begin{gathered} (x,y)=(-2,1) \\ \\ y=x+c \\ \\ 1=-2+c \\ \\ c=1+2 \\ \\ c=3 \end{gathered}`

So final equation of a line:

`\begin{gathered} y=mx+c \\ \\ m=1 \\ \\ c=3 \\ \\ y=x+3 \end{gathered}`

Equation of line is y = x + 3