2x+y-5=0;(0,4)write the standard form of the equation of the line that is parallel to the graph of the given equation and that passes through the point with the given coordinate.

Expert Answers
embizze eNotes educator| Certified Educator

We are given the line `2x+y-5=0` and a point (0,4) and we are asked to find the equation of a line through the point that is parallel to the given line.

The slope of a line in standard form `Ax+By+C=0` is `m=-A/B` . Thus the slope of the given line is m=-2

The slope of parallel lines is the same, so we seek the line through the point (0,4) with slope -2. We can use the point slope form : Given a point `(x_1,y_1)` and a slope m, the equation is `y-y_1=m(x-x_1)`

So the equation is `y-4=-2(x-0)==>y-4=-2x`


In standard form the equation is `2x+y-4=0`


The graphs of teh two lines:

ayush01 | Student

Here, equation of the given line: 2x+y-5=0

so slope of the line=-(coeficient of x/coefficient of y)



Slope of line parralel with this line is the same. Thus the slope of the required line(m)=-2

The line passes through (0,4),i.e, (x',y'). We have the formula to find the equation of a line when its slope is given and when a point on it is given as:


or y-4=-2(x-0)

or y-4=-2x

or, y=-2x+4

This is the required equation which is in the form of y=mx+c.