Question

The equation in standard form of a line that pssses through (-1,3) and has a slope of -3

Answer 1

The equation in standard form of a line that passes through (-1,3) and has a slope of -3 is
`\(3x + y = 0\).`

Step-by-step explanation:

The standard form of a linear equation is given by
`\(Ax + By = C\)` , where
`\(A\), \(B\), and \(C\)` are constants. To find the equation of a line passing through a given point
`\((-1,3)\)` with a specified slope of
`\(-3\)` , we can substitute these values into the standard form equation.

The slope-intercept form
`\(y = mx + b\)` provides insight into the slope
`(\(m\))` and the y-intercep
`t (\(b\))` . In this case, the slope is given as
`\(-3\)` , and substituting the coordinates of the point into the slope-intercept form leads to the standard form equation
`\(3x + y = 0\).`

Understanding the relationship between the slope and the coefficients in the standard form equation is essential in describing linear relationships. The coefficient of
`\(x\) (\(A\))` represents the slope, while the coefficient of
`\(y\) (\(B\))` captures the negative reciprocal of the slope. The constants
`\(A\), \(B\), and \(C\)` are chosen to satisfy the conditions of the line.

The point-slope form
`\(y - y_1 = m(x - x_1)\)` is a useful intermediate step in deriving the standard form equation. By substituting the given point
`\((-1,3)\)` and the slope
`\(-3\)` into this form, we can manipulate the equation to its standard form, providing a comprehensive representation of the line.