Write the equation for a line with y-intercept b=-2 and gradient m=5 in general form

1 answer

To write the equation of a line in general form given the y-intercept \( b = -2 \) and gradient \( m = 5 \), we start with the slope-intercept form of the line, which is:

\[ y = mx + b \]

Substituting the given values:

\[ y = 5x - 2 \]

Next, to convert this equation into general form \( Ax + By + C = 0 \), we will rearrange the terms:

\[ 5x - y - 2 = 0 \]

To express it in the standard format \( Ax + By + C = 0 \), we can rearrange further:

\[ 5x - y = 2 \]

Thus, in general form, the equation of the line is:

\[ 5x - y - 2 = 0 \]