Find the Line Equation: Parallel to 2(y+1)=16x Through Point (0,1)

Video Solution

Solution Steps

00:09 Let's find the algebraic representation of the function.

00:14 First, open the parentheses properly and multiply each factor. Take your time with this step.

00:24 Next, let's isolate Y. Focus on getting Y by itself on one side of the equation.

00:31 You've got it! This is the equation of the parallel function.

00:35 Remember, this is the slope of the parallel function.

00:39 Parallel functions have equal slopes, keep that in mind.

00:44 Let's use the line equation, which is a handy tool here.

00:48 Substitute the point according to the given data. You're doing great!

00:53 Now, substitute the slope and solve to find the intersection point, the point B.

01:02 This is the intersection point with the Y-axis.

01:10 Now, substitute this intersection point and the slope in the line equation.

01:23 Finally, arrange the equation nicely.

01:31 And there you have it, the solution to the question. Well done!

Step-by-Step Solution

To solve for the equation of the line parallel to $2(y+1)=16x$ that passes through the point $(0,1)$ , follow these steps:

Step 1: Convert the given line's equation to slope-intercept form. Start with $2(y+1) = 16x$ .
Step 2: Distribute and simplify to get $2y + 2 = 16x$ , which rearranges to $2y = 16x - 2$ .
Step 3: Solve for $y$ by dividing everything by 2: $y = 8x - 1$ . Hence, the slope $m$ is 8.
Step 4: Use the slope of 8 and the point $(0,1)$ in the point-slope form of a line equation:
$\quad y - y_1 = m(x - x_1)$
Step 5: Substitute the point $(0,1)$ and the slope $8$ :
$\quad y - 1 = 8(x - 0)$
Step 6: Simplify the expression
$\quad y - 1 = 8x$
Step 7: Rewrite the equation to achieve the desired form by moving 1 to the other side:
$\quad y = 8x + 1$
Step 8: To match the expected form, rewrite
$y - 8x = 1$

Therefore, the equation of the line that meets the criteria is given by $y - 8x = 1$ , corresponding to choice 3.