Question

What is the equation of the line in standard form that passes through the point (–1, 4) and is parallel to the line y = 2x – 3?

x – 2y = 6

x + 2y = 6

2x – y = –6

2x + y = –6

Answer 1

Once again. Here the line is parallel not perpendicular. When it's perpendicular, we take the negative reciprocal of the slope, but when the line is parallel, the slope stays the exact same. The only thing that changes is the b value. So from right there, we know that the equation will look something like y = 2x + b.

Since we know the line goes through point (-1, 4), we can plug in -1 for x and 4 for y and solve for b to get the equation of the line.

4 = 2(-1) + b
4 = -2 + b
4 + 2 =b
6 = b --> Now we have our b value.

So, the equation of the line becomes: y = 2x + 6. But this is in slope-intercept form, we want it in standard form. So we rearrange the equation so that the b value is isolated from the rest of the equation:

y = 2x + 6 --> 2x - y = -6

Therefore, the equation of the line in standard form is: 2x - y = -6