Answer:
y = - [tex]\frac{3}{2}[/tex] x + 6
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{3}{2}[/tex], hence
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute (6, - 3 ) into the partial equation
- 3 = - 9 + c ⇒ c = - 3 + 9 = 6
y = - [tex]\frac{3}{2}[/tex] x + 6 ← equation in slope- intercept form
The equation of the line with a slope of -3/2 passing through the point (6, -3) in slope-intercept form is expressed as [tex]y = \frac{-3}{2} x+10[/tex]
The formula for calculating the equation of a line in slope-intercept form is expressed as;
[tex]y = mx+b[/tex]
m is the slope
b is the y-intercept
Given the following parameters
m = -3/2
(x0, y0) =(6, -3)
Get the equation in the point-slope form first
[tex]y-(-3)=-3/2(x-6)\\y+3=-3/2(x-6)\\2(y+3) = -3(x-6)\\2y+6 = -3x + 16\\2y = -3x +16 - 6\\2y = -3x+10\\y = \frac{-3}{2} x+10[/tex]
Hence the equation in slope-intercept form is expressed as [tex]y = \frac{-3}{2} x+10[/tex]
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