# What is the slope intercept form of the line passing through (1,5)  with a slope of -1/2 ?

Apr 23, 2016

$y = - \frac{1}{2} x + \frac{11}{2}$

#### Explanation:

Standardised slope intercept form: $\text{ } y = m x + c$
Where $m$ is the gradient.

Given point$\to \left(x , y\right) = \left(1 , 5\right)$ so we have related values for $x \mathmr{and} y$

Given gradient $\to - \frac{1}{2}$

So our standardised form become$\text{ } y = - \frac{1}{2} x + c$
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We are given that when $y = 5 \text{ " x=1" }$ so by substitution we have:

" "color(brown)(y=-1/2x+c )color(blue)(" "->" "5=-1/2(1)+c)

Add $\frac{1}{2}$ to both sides

$\implies 5 + \frac{1}{2} = - \frac{1}{2} + \frac{1}{2} + c$

$\implies \frac{11}{2} = 0 + c$

$\implies c = \frac{11}{2}$
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Thus$\text{ "color(brown)(y=mx+c)color(blue)(" "->" } y = - \frac{1}{2} x + \frac{11}{2}$