Certainly! Let's derive the equation of the line step-by-step.
1. Identify the general form of the equation:
The general form of the equation for a straight line is:
[tex]\[
y = mx + c
\][/tex]
where [tex]\( m \)[/tex] is the slope of the line, and [tex]\( c \)[/tex] is the y-intercept.
2. Specify the values of the slope ([tex]\( m \)[/tex]) and the y-intercept ([tex]\( c \)[/tex]):
- The slope, [tex]\( m \)[/tex], has been identified as [tex]\( \frac{2}{3} \)[/tex].
- The y-intercept, [tex]\( c \)[/tex], has been identified as [tex]\( \frac{5}{7} \)[/tex].
3. Substitute the values into the general form:
- Substituting [tex]\( m = \frac{2}{3} \)[/tex] and [tex]\( c = \frac{5}{7} \)[/tex] into the general form, we get:
[tex]\[
y = \frac{2}{3}x + \frac{5}{7}
\][/tex]
4. Write the final equation:
Thus, the equation of the line in its simplest form is:
[tex]\[
y = \frac{2}{3}x + \frac{5}{7}
\][/tex]
This is the equation of the line, with [tex]\( m \)[/tex] and [tex]\( c \)[/tex] as fractions in their simplest forms.
