graph a line parallel to 2x-4y=5

Question

graph a line parallel to the line 2x-4y=5 that contains the point (0,3). Write the equation of the line in standard form. Label all the intercepts of the line

Answer 1

First you need to figure out the slope of the given line (2x - 4y =5) by putting it in slope intercept form (y = mx + b).

subtract 2x from both sides to get -4y = -2x - 5
divide both sides by -4 to get y = (1/2)x + (5/4)
So the slope of this line is 1/2.

Any lines that are parallel to this line will have the same slope of 1/2.  Using this slope and the given point (0,3) you can plug this information into the point slope form of a line [y - y1 = m(x - x1)] to get the equation of the line you are looking for.

y - 3 = (1/2)(x - 0)
Use distributive property on the right hand side to get y - 3 = (1/2)x
Subtract y from both sides to put into standard form to get (1/2)x - y = -3

The x-intercept of a line is the x value when y is 0.  If you plug in 0 for y you have (1/2)x = -3.  Multiply both sides by 2 to solve for x and you get that the x-intercept is (-6,0).

The y-intercept of a line is the y value when x is 0.  If you plug in 0 for x you have that -y = -3.  Divide both sides by -1 to solve for y and you get that the y-intercept is (0,3).