Answer:
[tex] y = \frac{1}{2}x + \frac{1}{4} [/tex]
Step-by-step explanation:
Equation in slope-intercept form is given as [tex] y = mx + b [/tex]
An equation parallel to [tex] y = \frac{1}{2}x + \frac{5}{2} [/tex] would have the same slope as the equation.
The slope (m) of the line would be ½.
m = ½.
Given that this same line runs through or contains (³/2, 1), we cam find the value of b (y-intercept) by substituting m = ½, x = ³/2, and y = 1 in [tex] y = mx + b [/tex].
Thus:
[tex] 1 = (\frac{1}{2})(\frac{3}{2}) + b [/tex]
[tex] 1 = \frac{3}{4} + b [/tex]
Subtract both sides by ¾
[tex] 1 - \frac{3}{4} = b [/tex]
[tex] \frac{1}{4} = b [/tex]
To derive the equation, substitute m = ½, and b = ¼ in [tex] y = mx + b [/tex].
✔️The equation is:
[tex] y = \frac{1}{2}x + \frac{1}{4} [/tex]
