Question 83·Medium·Linear Functions

Parallel lines have the same slope. Once you know the slope of the original line, your new line must use that exact slope.

Plug the slope and the point $(3,-2)$ into point-slope form $y - y_1 = m(x - x_1)$, then rearrange the equation into $y=mx+b$ so you can compare it with the answer choices.

In a new expression line, type y=2x-3 to graph a line equivalent to $4x-2y=6$. This helps you see the slope and orientation of the given line.

In separate expression lines, enter each choice exactly as written: y=-1/2x+1/2, y=2x+8, y=-2x-8, and y=2x-8. You should now see four candidate lines along with the original line.

Add the point (3,-2) in Desmos. Look for which of the four candidate lines passes through this point and has the same tilt (slope) as the original line y=2x-3. The equation of that line is the correct choice.

Rewrite the given equation $4x-2y=6$ in slope-intercept form $y=mx+b$.

Start by isolating $y$:

So the slope of the given line is $m=2$.

Any line parallel to the given line must have the same slope $m=2$.

Use point-slope form with the point $(3,-2)$ and slope $2$:

So we have:

Now simplify $y + 2 = 2(x - 3)$ to get it into $y=mx+b$ form:

This matches answer choice D) $y=2x-8$, so that is the equation of the line that is parallel to $4x-2y=6$ and passes through $(3,-2)$.