The standard form of a linear equation is typically expressed as \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \) is non-negative.
To find the equation in standard form for the point \( (5, -10) \), we first interpret this point as a solution to an equation. However, with just one point, we can create a line that passes through it.
We can use the slope-intercept form, \( y = mx + b \), to find the line through this point. Since we only have the one point, we can choose a slope \( m \). A simple case is to consider a vertical line where \( x = 5 \), which is the simplest form that can be derived from the point.
To convert this vertical line into the standard form:
- A vertical line's equation can be represented as \( x = a \).
- The standard form would then imply rearranging it to fit \( Ax + By = C \).
For the vertical line \( x = 5 \):
- It can be rewritten in standard form as: \[ 1x + 0y = 5 \] This corresponds to \( A = 1 \), \( B = 0 \), and \( C = 5 \).
If you want a different linear equation that goes through the point \( (5, -10) \) with a specific slope, let me know, and I can help you construct that equation in standard form as well.