To determine the equation of a straight line, we can use the general form of a linear equation, which is:
[tex]\[ y = mx + c \][/tex]
In this equation, [tex]\( m \)[/tex] represents the gradient (or slope) of the line, and [tex]\( c \)[/tex] is the y-intercept (the point where the line crosses the y-axis).
Given Data:
- The gradient [tex]\( m \)[/tex] is provided as 5.
- The line passes through the point [tex]\((0, -3)\)[/tex].
Since the line passes through the point [tex]\((0, -3)\)[/tex], we know that the y-intercept [tex]\( c \)[/tex] is -3. This is because when [tex]\( x = 0 \)[/tex], the value of [tex]\( y \)[/tex] directly gives us the y-intercept in the equation [tex]\( y = mx + c \)[/tex].
Therefore, substituting the gradient and the y-intercept into the equation of the line:
[tex]\[ y = 5x - 3 \][/tex]
So, the equation of the straight line [tex]\( L \)[/tex] is:
[tex]\[ y = 5x - 3 \][/tex]
