Problem

Find the equation of the line parallel to the line 3x−4y=8 and passing through the point (4,2).

Answer

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Answer

Step 4: Substitute the slope and y-intercept into the equation y=mx+b to get the equation of the line.

Steps

Step 1 ：Step 1: Rewrite the given line in slope-intercept form, y=mx+b, to find the slope. Adding 4y to both sides and then dividing by 4 gives y=34x−2. So the slope of the given line is 34.

Step 2 ：Step 2: Since parallel lines have the same slope, the line we are looking for also has a slope of 34.

Step 3 ：Step 3: Using the slope-intercept form y=mx+b, substitute the given point (4,2) and the slope 34 into the equation to find the y-intercept b. This gives 2=34∗4+b, so b=−1.

Step 4 ：Step 4: Substitute the slope and y-intercept into the equation y=mx+b to get the equation of the line.

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