Equation of a Straight Line Passing Through (-1,2) and Distance from Origin is One Unit

To find the equation of a straight line passing through the point (-1,2) and with a distance of one unit from the origin, we can follow these steps:

Step 1: Determine the Slope of the Line
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Since we know that the line passes through (-1,2) and the origin (0,0), we can substitute these values into the formula:

m = (0 - 2) / (0 - (-1))
m = -2 / 1
m = -2

Step 2: Use the Point-Slope Form
The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

Substituting the values we have:

y - 2 = -2(x - (-1))

Simplifying the equation:

y - 2 = -2(x + 1)
y - 2 = -2x - 2
y = -2x - 2 + 2
y = -2x

So the equation of the line passing through the point (-1,2) and with a distance of one unit from the origin is y = -2x.

Explanation:
We start by finding the slope of the line using the coordinates of the two given points, (-1,2) and the origin (0,0). By substituting these values into the slope formula, we determine that the slope (m) is -2.

Then, we use the point-slope form of a linear equation to write the equation of the line. We substitute the coordinates of the given point (-1,2) into the point-slope form equation and simplify to obtain the final equation.

The line y = -2x represents a straight line with a slope of -2. It passes through the point (-1,2) and has a distance of one unit from the origin.

2x-y+2=0