What is the equation of the line parallel to $4x+2y=8$ and passing through the point $(0,1)$? Write the equation in slope-intercept form.
I know that parallel lines have the same slope, so I can use the slope of the given line to find the slope of the parallel line. To find the slope of the given line, I can rearrange it into slope-intercept form by solving for $y$. Subtracting $4x$ from both sides, I get $2y=-4x+8$. Dividing both sides by $2$, I get $y=-2x+4$. Now I can see that the slope of the given line is $-2$, so the slope of the parallel line is also $-2$. To find the equation of the parallel line, I can use the point-slope form, which is $y-y_1=m(x-x_1)$, where $m$ is the slope and $(x_1,y_1)$ is the given point. Plugging in the values, I get $y-1=-2(x-0)$. Simplifying, I get $y=-2x+1$. This is the equation of the parallel line in slope-intercept form. 