Question

1. Write an equation in slope intercept form for the line that passes through (-2,2) and is parallel to 2x+4y= 16

2. Write an equation in slope intercept form for the line that passes through (4,1) and is perpendicular to 4x -y=3

Answer 1

The equation of this line would be y = -1/2x + 1

Explanation:

In order to find this equation we must first find the slope of the original line. To do this, we need to solve the original equation for y.

2x + 4y = 16

4y = -2x + 16

y = -1/2x + 4

The original slope (the coefficient of x) is -1/2, which means the new slope will also be -1/2 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.

y - y1 = m(x - x1)

y - 2 = -1/2(x + 2)

y - 2 = -1/2x - 1

y = -1/2x + 1