Question

A line that passes through the point $(0,1)$ is parallel to
$2x+y=3$. What is its equation?

• A. $y=2x+1$
• B. $y=-2x+1$
• C. $y=2x+3$
• D. $y=-2x+3$

Answer 1

The correct option is B $y=-2x+1$

The slope-intercept form of a line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept of the line.
We need to find the equation of the line that is parallel to $2x+y=3$ and passes through the point $(0,1)$.

We first need to write $2x+y=3$ in standard form.
$2x+y=3$
$\Rightarrow y=-2x+3$
The slope of the above ine is $-2$ and its y-intercept is $3$.

Any line parallel to the above line will have slope $-2.$
So, the slope of the required line is $-2.$
The line also passes through $(0,1)$.
As the x-coordinate of the point is 0, it means it lies on the y-axis with y-coordinate $1$.
This means its y-intercept is $1.$
$\Rightarrow b=1$

The equation of the required line wil be $y=-2x+1$.