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