To find the equation of the line in the form \(\(y = -3x + b\)\), we need to determine the y-intercept, \(\(b\)\).
The given line equation is \(\( y = -3x + b \)\), where the slope \(\( m \)\) is -3.
The slope-intercept form of a line equation is \(\( y = mx + b \)\), where:
- \(\( m \)\) is the slope,
- \(\( b \)\) is the y-intercept.
In this case, the slope \(\(m\)\) is given as -3. To find the y-intercept \(\(b\)\), we need a point \(\((x, y)\)\) that the line passes through.
Assume the line passes through the origin, which is the point \(\( (0, 0) \)\). By substituting \(\((x, y)\)\) = (0, 0) into the equation:
\(\[ y = -3x + b \]\)
we get:
\(\[ 0 = -3(0) + b \]\)
Simplifying the above equation:
\(\[ 0 = 0 + b \]\)
Thus:
\(\[ b = 0 \]\)
So, the y-intercept \(\( b \)\) is 0. Therefore, the equation of the line simplifies to:
\(\[ y = -3x + 0 \]\)
or simply:
\(\[ y = -3x \]\)
This indicates that the line passes through the origin and has a slope of -3.
