Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (5, 1 ) into the partial equation
1 = [tex]\frac{5}{2}[/tex] + c ⇒ c = 1 - [tex]\frac{5}{2}[/tex] = - [tex]\frac{3}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] ← equation of line
to find the y- intercept , let y = 0 in the equation , that is
[tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] = 0 ( multiply through by 2 to clear the fractions )
x - 3 = 0 ( add 3 to both sides )
x = 3 ← is the x- intercept
from the equation the y- intercept is the value of c , then
y- intercept = - [tex]\frac{3}{2}[/tex]
