Question

Which equation represents a line that is parallel to the line y=3-2x?1) 4X+ 2Y=52)2x+4y=13)y=3-4X 4)y=4X-2

Answer 1

A general equation for a line in the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Given the equation:

y = 3 - 2x

Which, in the slope-intercept form is:

y = -2x + 3

That is, the slope is -2.

To find the parallel line, let's write the options in the slope-intercept form too. Parallel lines have the same slope.

1) 4x + 2y = 5

To put it in the slope-intercept form, let's subtract 4x from both sides and then divide the sides by 2:

`\begin{gathered} 4x+2y-4x=5-4x \\ 2y=-4x+5 \\ (2)/(2)y=(-4x+5)/(2) \\ y=-2x+5 \end{gathered}`

Slope = -2. The lines have the same slope (-2) and thus are parallels.

2) 2x + 4y = 1

To put it in the slope-intercept form, let's subtract 2x from both sides and then divide the sides by 4:

`\begin{gathered} 2x+4y-2x=1-2x \\ (4)/(4)y=(-2x+1)/(4) \\ y=-(1)/(2)x+(1)/(4) \end{gathered}`

Slope = -1/2.

The equations have different slopes. So, they are not parallel.

3) y = 3 - 4x

To write it in the slope-intercept form, just organize the order of the terms on the second side of the equation.

`y=-4x+3`

Slope = -4.

The equations have different slopes. So, they are not parallel.

4) y = 4x - 2

The equation is in the slope-intercept form.

Slope 4. The equations have different slopes. So, they are not parallel.

Answer: 4x+ 2y = 5 is parallel to y = 3 - 2x.