Answer:
[tex]y = \frac{1}{2} x + \frac{1}{2} [/tex]
Step-by-step explanation:
equation of line formula:
[tex]y = mx + c[/tex]
m = slope
c = y-intercept
1) find m
slope formula:
[tex]m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}} [/tex]
take 2 coordinates from the given graph and substitute the values into the slope formula
i) (-1,0)
[tex]x _{1} = - 1[/tex]
[tex]y_{1} = 0[/tex]
ii) (3,2)
[tex]x_{2} = 3[/tex]
[tex]y_{2} = 2[/tex]
substitute the values into the slope formula
[tex]m = \frac{2 - 0}{3 - ( - 1)} [/tex]
[tex]m = \frac{2}{4} [/tex]
[tex]m = \frac{1}{2} [/tex]
2) find the half equation of the line by substituting the value of m into the equation of line formula
[tex]y = \frac{1}{2} x + c[/tex]
3) find c by substituting either coordinate into the half equation
(3,2)
x = 3
y = 2
[tex]2 = \frac{1}{2} (3) + c[/tex]
[tex]2 = \frac{3}{2} + c[/tex]
[tex]2 - \frac{3}{2} = c[/tex]
[tex] \frac{1}{2} = c [/tex]
[tex]c = \frac{1}{2} [/tex]
4) find equation of line by substituting the value of c into the half equation
[tex]y = \frac{1}{2} x + \frac{1}{2} [/tex]
