Find the equation of the line (in slope intercept form) through (-5,8) and perpendicular to the line 4x + 2y = 8
We re-write the equation in slope-intercept form to find the slope of the ``equation. `4x+2y=8` We subtract 4x from each side and get `2y=8-4x=-4x+8` We divide both sides by 2 and its `y=-2x+4`
The equation we seek is perpendicular to this so its slope should be the negative reciprocal of -2, which is `1/2`
Now that we know the slope(m), we can find the intercept (b) by inserting the ordered pair (-5,8) into the equation y=mx+b
`y=mx+b->8=1/2(-5)+b=-2 1/2+b` We add `2 1/2` to each side and we get `10 1/2=b`
The equation in slope intercept form is `y=1/2 x+10 1/2`
The equation of a line in slope intercept form is y = mx + c where m is the slope and c is the intercept.
Rewrite the equation of the line 4x + 2y = 8 to determine its slope.
2y = 8 - 4x
y = -2x + 4
The slope of this line is -2.
As we have to determine the equation of a line perpendicular to this line remember that the product of slope of two perpendicular lines is -1.
The slope of the required line is 1/2.
As it passes through the point (-5,8).
(y - 8)/(x + 5) = 1/2
y - 8 = x/2 + 5/2
y = x/2 + 21/2
The required equation is y = x/2 + 11.5