Write an equation in slope-intercept form for the line.
1. Perpendicular to 5x + 2y = 8 and through (5,3).
A: y = -1/5x + 4?
2 y = -5 x + 8
y = -(5/2) x + 4
slope = -5/2 so slope of perpendicular = 2/5
y = -(2/5) x + b
3 = -(2/5)5 + b
3 = -2 + b
b = 5
y = -(2/5) x + 5
Wouldn't the slope be -1/5?
nope,,
Damon showed you that the slope of your given line is -5/2
Trust him !
To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line is 5x + 2y = 8. We can rearrange this equation to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
2y = -5x + 8
y = -5/2x + 4
The slope of the given line is -5/2.
To find the slope of a line perpendicular to this, we take the negative reciprocal of -5/2. The negative reciprocal is the opposite sign of the fraction and the reciprocal (flipping the numerator and denominator):
(-5/2) --> (2/5)
So, the slope of the line perpendicular to 5x + 2y = 8 is 2/5.
Now that we have the slope (m = 2/5) and a point on the line (5,3), we can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
Substituting the values, we have:
y - 3 = (2/5)(x - 5)
Expanding and rearranging the equation:
y - 3 = (2/5)x - 2
y = (2/5)x + 1
Therefore, the equation of the line perpendicular to 5x + 2y = 8 and passing through the point (5,3) is y = (2/5)x + 1.