First we wanna convert x + 2y = 14 into a slope-intercept equation.
x + 2y = 14
2y = 14 - x
y = 7 - x/2 or y = -1/2x + 7
Now that we have the line in slope-intercept form, we can solve for a line that is parallel to.
But first, what do parallel lines have in common? Parallel lines never intersect first of all and second they have the same slope so meaning we’re going to use -1/2 in order to find the equation of a parallel line so…
y = -1/2x + b
use the given point in the question
0 = -1/2(-8) + b
0 = 4 + b
b = 0 - 4
b = -4
The y-intercept of the line is -4
The equation of the line that passes through the point (-8, 0) and is parallel to the line x + 2y = 14 is y = -1/2x - 4
Given that the goat pasture is rectangular with the dimensions given by: Length=(y-4) and Width=(4y^2-3y+5) Thus the area of the pasture will be given: Area=length*width Area=(4y^2-3y+5)(y-4) Area=y(4y^2-3y+5)-4(4y^2-3y+5) Area=4y^3-19y^2+17y-20
