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
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).