Final answer:
The y-intercept of the line is -17.
Step-by-step explanation:
To find the y-intercept of the line that passes through the point (4, -9) and is perpendicular to the line x + 2y = 4, we first need to determine the slope of the line given by x + 2y = 4. We can rewrite this equation in slope-intercept form (y = mx + b) by solving for y:
2y = -x + 4
y = -0.5x + 2
The slope of this line is -0.5. Since the line we are interested in is perpendicular, its slope will be the negative reciprocal of -0.5, which is 2.
Next, we can use the point-slope form of a linear equation (y - y1 = m(x - x1)) to find the equation of the perpendicular line:
y - (-9) = 2(x - 4)
y + 9 = 2x - 8
y = 2x - 17
So, the y-intercept of the line that passes through the point (4, -9) and is perpendicular to the line x + 2y = 4 is -17.