Answer
So, the equation of the line perpendicular to x+2y=4 and passing through the point (−4,−7) is y=2x+1.
Step by Step
To find the equation of a line perpendicular to x+2y=4 and passing through the point (−4,−7), we'll first find the slope of the given line and then determine the negative reciprocal to get the slope of the perpendicular line.
The Equation x+2y=4 can be written in slope-intercept form (y=mx+b) by solving for y:
x+2y=4
2y=−x+4
y=-1/2x+2
So, the slope of the given line is -1/2 The negative reciprocal of -1/2 is 2 which will be the slope of the perpendicular line.
Now, we can use the point-slope form of a line to find the equation of the perpendicular line:
y-y1=m(x-x1)
Using the point (−4,−7) and the slope m=2
y−(−7)=2(x−(−4))
Simplify the equation: y+7=2(x+4)
Distribute 2 on the right side: y+7=2x+8
Subtract 7 from both sides to isolate y=2x+1
So, the equation of the line perpendicular to x+2y=4 and passing through the point (−4,−7) is y=2x+1.