To find the equation of a line that is parallel to the given line [tex]\( y = 9x - 4 \)[/tex] and passes through the point [tex]\( (2, 7) \)[/tex], we need to follow these steps:
1. Identify the Slope of the Given Line:
The slope-intercept form of a line is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope. The given line has the equation [tex]\( y = 9x - 4 \)[/tex], so the slope [tex]\( m \)[/tex] is 9.
2. Determine the Slope of the Parallel Line:
Parallel lines have equal slopes. Therefore, the slope of our new line will also be 9.
3. Use the Point-Slope Form to Write the Equation:
The point-slope form of a line's equation is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Here, [tex]\( (x_1, y_1) \)[/tex] is the point through which the line passes, and [tex]\( m \)[/tex] is the slope. Substituting the given point [tex]\( (2, 7) \)[/tex] and the slope 9, we get:
[tex]\[
y - 7 = 9(x - 2)
\][/tex]
4. Final Step:
The equation of the line in point-slope form that passes through the point (2, 7) and is parallel to [tex]\( y = 9x - 4 \)[/tex] is:
[tex]\[
y - 7 = 9(x - 2)
\][/tex]
Hence, the value that belongs in the green box is 7.
So the completed equation in the desired format is:
[tex]\[
y - 7 = 9(x - 2)
\][/tex]
