# Determine the equation of the line that passes through the point (–5,3) and has slope (-1/2) ; write the equation in standard form.

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The equation of a line can be given in the standard form as;

`ax+by = c`

If we know the slope of a line we can write the linear equation in the slope intercept form as `y = mx+c`

For our given question `m = (-1/2)` .

It is given that the line passes through point `(-5,3)` .

`y = (-1/2)x+c`

`3 = (-1/2)(-5)+c`

`c = 3+5/2`

`c = 11/2`

`y = (-1/2)x+11/2`

`2y = -x+11`

`x+2y = 11`

*So the answer in standard form is x+2y = 11*

We need to find the equation of the line that passes through the point (–5,3) and has slope (-1/2) ; and write the equation in standard form.

Given point and slope, lets first write in point-slope form:

y - 3 = (-1/2)(x + 5)

Multiply by -2 to get rid of the fraction and negative slope:

-2y + 6 = x + 5

Rearrange so that x and y are on the same side:

x + 2y = 1