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

Question

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Respuesta :

ParisL471696 ParisL471696 · Answer 1 · 2022-10-31T02:07:31+01:00

Given:

Find-:

Equation of a line.

Sol:

General equation of a line.

[tex]y=mx+c[/tex]

Where,

[tex]\begin{gathered} m=\text{ slope} \\ \\ m=\frac{x_2-x_1}{y_2-y_1} \\ \\ c=\text{ y-intercept.} \end{gathered}[/tex]

Choose any two-point then:

[tex]\begin{gathered} (-2,1)=(x_1,y_1) \\ \\ (-1,2)=(x_2,y_2) \end{gathered}[/tex]

So the slope of the line is:

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{2-1}{-1-(-2)} \\ \\ m=\frac{1}{-1+2} \\ \\ m=1 \end{gathered}[/tex]

So the equation become:

[tex]\begin{gathered} y=mx+c \\ \\ y=(1)x+c \\ \\ y=x+c \end{gathered}[/tex]

So y-intercept is:

[tex]\begin{gathered} (x,y)=(-2,1) \\ \\ y=x+c \\ \\ 1=-2+c \\ \\ c=1+2 \\ \\ c=3 \end{gathered}[/tex]

So final equation of a line:

[tex]\begin{gathered} y=mx+c \\ \\ m=1 \\ \\ c=3 \\ \\ y=x+3 \end{gathered}[/tex]

Equation of line is y = x + 3