To complete the slope-intercept form of the line given, we need to determine the y-intercept based on the provided information.
The slope-intercept form of a line is defined as:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
From the data provided, we know:
[tex]\[ m = -4 \][/tex]
And we also have a point on the line:
[tex]\[ (-2, 17) \][/tex]
To find the y-intercept, we can substitute the values of the slope ([tex]\( m \)[/tex]), and the coordinates of the point ([tex]\( x_1 = -2 \)[/tex] and [tex]\( y_1 = 17 \)[/tex]) into the slope-intercept formula:
[tex]\[ y = mx + b \][/tex]
Rearranging the formula to solve for [tex]\( b \)[/tex]:
[tex]\[ b = y - mx \][/tex]
Substitute [tex]\( y = 17 \)[/tex], [tex]\( m = -4 \)[/tex], and [tex]\( x = -2 \)[/tex]:
[tex]\[ b = 17 - (-4 \cdot -2) \][/tex]
[tex]\[ b = 17 - 8 \][/tex]
[tex]\[ b = 9 \][/tex]
Therefore, the complete slope-intercept form of the line is:
[tex]\[ y = -4x + 9 \][/tex]
The equation of the line is:
[tex]\[ y = -4x + 9 \][/tex]
