Question

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Answer 1

Answer:

$y = \frac{1}{2} x + \frac{1}{2}$

Step-by-step explanation:

equation of line formula:

$y = mx + c$

m = slope

c = y-intercept

1) find m

slope formula:

$m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}}$

take 2 coordinates from the given graph and substitute the values into the slope formula

i) (-1,0)

$x _{1} = - 1$

$y_{1} = 0$

ii) (3,2)

$x_{2} = 3$

$y_{2} = 2$

substitute the values into the slope formula

$m = \frac{2 - 0}{3 - ( - 1)}$

$m = \frac{2}{4}$

$m = \frac{1}{2}$

2) find the half equation of the line by substituting the value of m into the equation of line formula

$y = \frac{1}{2} x + c$

3) find c by substituting either coordinate into the half equation

(3,2)

x = 3

y = 2

$2 = \frac{1}{2} (3) + c$

$2 = \frac{3}{2} + c$

$2 - \frac{3}{2} = c$

$\frac{1}{2} = c$

$c = \frac{1}{2}$

4) find equation of line by substituting the value of c into the half equation

$y = \frac{1}{2} x + \frac{1}{2}$