The line that is parallel to 8+2y=1+4x and goes through the point (3,15) is?

To find the line that is parallel to 8+2y=1+4x and goes through the point (3,15), we first need to find the slope of the given line.

Rearranging the equation 8+2y=1+4x into slope-intercept form (y=mx+b), we get:
2y = 4x - 7
y = 2x - 3.5

The slope of this line is 2.

Since the line we are looking for is parallel to this line, it will have the same slope of 2.

Now, using the point-slope form of a linear equation (y-y1 = m(x-x1)), we can plug in the values of the point (3,15) and the slope (2) to find the equation of the line:

y - 15 = 2(x - 3)
y - 15 = 2x - 6
y = 2x + 9

Therefore, the line that is parallel to 8+2y=1+4x and goes through the point (3,15) is y = 2x + 9.

Step 1: Find the slope of the given line.

The given line is 8y = 14x. To put it in slope-intercept form (y = mx + b), divide both sides by 8:

y = (14/8)x
y = (7/4)x

So, the slope of the given line is 7/4.

Step 2: Since parallel lines have the same slope, the slope of the line parallel to it is also 7/4.

Step 3: Use the point-slope form to find the equation of the parallel line.

The point-slope form of a line is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Substituting the given point (3, 15) and the slope 7/4:

y - 15 = (7/4)(x - 3)

Step 4: Simplify the equation to get the line in slope-intercept form.

y - 15 = (7/4)x - (21/4)
y = (7/4)x - (21/4) + 15
y = (7/4)x - (21/4) + (60/4)
y = (7/4)x + (39/4)

Therefore, the line that is parallel to 8y = 14x and goes through the point (3, 15) is y = (7/4)x + (39/4).