Question

You want to find the equation for a line that passes through the point (3,-4) and has a slope of -1/2.

Answer 1

`y = -(1)/(2)x -(5)/(2)`

Explanation:

We are given;

• A point where the line is passing through as (3, -4)
• The slope of the line -1/2

We are required to determine the equation of the line;

• Note that, one way we can get the equation of a straight line is when we are given a point where the line is passing through and its slope.
• Thus, in this case, we can determine the equation;

Taking another point (x, y)

Then; (x, y) , ( 3, -4) and slope -1/2 can give us the equation;

That is;

`(y+4)/(x-3)=-(1)/(2)`

Cross multiplication;

`2(y+4) = -1 (x-3)`

`2y + 8 = -x +3`

Combining the like terms;

`2y=-x-5\\y = -(1)/(2)x-(5)/(2)`

Thus, the equation of the line is;
`y = -(1)/(2)x -(5)/(2)`