Question

What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)? y = –x + 33y = –x + 36y = 4x − 16y = 4x + 16?

Answer 1

Solution:

D is the correct option.

Explanation:

The equation for the given line is y − 1 = 4(x + 3). Let us convert this equation in slope intercept form y= mx +b, where m is slope and b is the y-intercept.

$y- 1 = 4(x + 3)\\\\y-1=4x+12\\\\y=4x+13$

Thus, the slope of this line is 4.

Now, we know that the slope of parallel lines are equal. Hence, the slope of the required line is same as the slope of the given line.

Hence, the slope of the required line is m = 4

It passes through the point (4,32).

The point slope form of a line is given by

$y-y_1=m(x-x_1)\\y-32=4(x-4)\\y-32=4x-16\\\\y=4x+16$

Therefore the equation of the line is y = 4x+16

D is the correct option.

Answer 2

The equation of line that is parallel to the line $y-1=4\left({x+3}\right)$   and passes through the point $\left({4,32}\right)$  is $\boxed{{\mathbf{y=4x+16}}}$  and it matches with $\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}$ .

Further explanation:

It is given that the equation of line is $y-1=4\left({x+3}\right)$  and passes through point $\left({4,32}\right)$ .

Rewrite the given equation $y-1=4\left({x+3}\right)$  as follows:

$\begin{aligned}y-1&=4\left({x+3}\right)\\y-1&=4x+12\\y&=4x+12+1\\y&=4x+13\\\end{aligned}$

Now, compare the obtained equation of line $y=4x+13$  with the standard equation of line $y=mx+b$ .

$\begin{aligned}m&=4\\b&=13\\\end{aligned}$

Therefore, the slope is $4$  and the intercept is 13.

It is given that both lines are parallel to each other so the product of both slopes must be equal.

Substitute $4$  for ${m_1}$  in equation ${m_1}={m_2}$  to obtain the value of slope ${m_2}$ .

 ${m_2}=4$

Therefore, the slope is $4$ .

It is given that the line passes through point $\left({4,32}\right)$ .

The point-slope form of the equation of a line with slope $m$  passes through point $\left({{x_1},{y_1}}\right)$ is represented as follows:

$y-{y_1}=m\left({x-{x_1}}\right)$                                    …… (2)

Substitute $4$  for ${x_1}$ , $32$  for ${y_1}$  and  $4$ for $m$  in equation (2) to obtain the equation of line.

$\begin{aligned}y-32&=4\left({x-4}\right)\\y-32&=4x-16\\y&=4x-16+32\\y&=4x+16\\\end{aligned}$

Therefore, the equation of line is $y=4x+16$ .

Now, the four options are given as follows.

$\begin{gathered}{\text{OPTION A}}\to y=-x+33\hfill\\{\text{OPTION B}}\to y=-x+36\hfill\\{\text{OPTION C}}\to y=4x-16\hfill\\{\text{OPTION D}}\to y=4x+16\hfill\\\end{gathered}$

Since OPTION D matches equation of line that is $y=4x+16$ .

Thus, the equation of line that is parallel to the line  $y-1=4\left({x+3}\right)$ and passes through the point $\left({4,32}\right)$  is $\boxed{{\mathbf{y=4x+16}}}$  and it matches with $\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}$ .

Learn more:

1. Which classification best describes the following system of equations? brainly.com/question/9045597

2. What is the value of $x$  in the equation $x-y=30$  when $y=15$ ? brainly.com/question/3965451

3. What are the values of x? brainly.com/question/2093003

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, equation of line, line, passes through point, $y=4x+16$ .