Question

What is the equation of the line that is parallel to the given line and passes through the point (2, 3)?

A.) x + 2y = 4
B.) x + 2y = 8
C.) 2x + y = 4
D.) 2x + y = 8

Answer 1

`\text{The formula of a slope:}\\\\m=(y_2-y_1)/(x_2-x_1)\\\\\text{We have the points (-4, 0) and (4, -4)}\\\\\text{substitute:}\\\\m=(-4-0)/(4-(-4))=(-4)/(8)=-0.5\\\\\text{therefore we have the equation of the given line in slope-intercept form:}\\y=-0.5x+b.\\\\\text{Parallel lines have the same slope.}\\\\\text{Therefore the line equation from question is y = -0.5x + b.}`

`\text{It passes through the point (2, 3).}\\\\\text{Substitute the coordinates of the given point  to the equation of the line}:\\\\3=-0.5(2)+b\\3=-1+b\qquad|+1\\4=b\to b=4\\\\\text{therefore}\ y=-0.5x+4\qquad|+0.5x\\\\0.5x+y=4\qquad|\cdot2\\\\\boxed{x+2y=8\to B.)}`