Write an equation of the line containing the point and perpendicular (4,-8);2x+5y=4. I still don't get it. I really appreciate your help.
2x + 5y = 4
Add -2x to both sides
5y = -2x + 4
divide both sides by 5
y = -2/5 y + 4/5
So, slope m = -2/5
Perpendicular lines, the slopes are negative reciprocals of each other.
Slope = -2/5
m1 * m2 = -1
-2/5 * m2 = -1
m2 = -1/(-2/5)
m2 = 5/2
Now you have to find b, for the equation of the perpendicular line.
y = mx + b
m = 5/2
y = 5/2 x + b
P(4, -8)
-8 = 5/2 (4) + b
-8 = 20/2 + b
-8 = 10 + b
-18 = b
y = 5/2 x + b
y = 5/2 + -18
y = 5/2 - 18
Follow these exact steps.
Esther, check your 1-26,2
Esther, check your 1-26,2:54am post.
To find the equation of a line that is perpendicular to another line, you need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
In this case, you're given the equation of a line, 2x+5y=4. To find the slope of this line, we need to rewrite the equation in slope-intercept form, which is in the form of y = mx + b, where m represents the slope.
So, let's rearrange the given equation to solve for y:
2x + 5y = 4
5y = -2x + 4
y = (-2/5)x + 4/5
From this equation, we can see that the slope of the given line is -2/5.
To find the slope of the perpendicular line, we take the negative reciprocal of -2/5. The negative reciprocal is found by flipping the fraction and changing the sign. So in this case, the slope of our perpendicular line would be 5/2.
Now that we have the slope of the perpendicular line (5/2) and a point it passes through (4, -8), we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Using the values we have:
y - (-8) = (5/2)(x - 4)
Simplifying,
y + 8 = (5/2)x - 10
y = (5/2)x - 18
Therefore, the equation of the line containing the point (4, -8) and perpendicular to the line 2x + 5y = 4 is y = (5/2)x - 18.