Question

Q1Find the equation of the line passing through the point (-3.6, 2.1) and parallel to the line 4.9x + 5.4y = 3


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Answer 1

Given:

(-3.6,2.1) and line 4.9x + 5.4y = 3

To find:

Find the equation of line passing through the point and parallel to the given line.

Solution:

We know that

Equation of a line passing through a point

$(x_1,y_1)$

1is given by

$\begin{gathered}\boxed{\bold{y-y_1=m(x-x_1)}}\\\end{gathered}$

here point is (-3.6,2.1)

So,

$\begin{gathered}y-2.1=m(x+3.6)\\\end{gathered}$

Now, find the slope of line.

We know that if two lines are parallel,then their slopes are equal.

Write line 4.9x + 5.4y = 3 in slope-intercept form; y=mx+c

$\begin{gathered}5.4y = - 4.9x + 3 \\ \\ y = \frac{ - 4.9}{5.4} x + \frac{3}{5.4} \\ \\ y = \frac{ - 49}{54} x + \frac{3}{5.4} \\\end{gathered}$

Slope (m)= -49/54

Put the value of slope in eq1

$\begin{gathered}y-2.1= \frac{ - 49}{54} (x+3.6)\\ \\ 54(y - 2.1) = - 49(x + 3.6) \\ \\ 54y - 113.4 = - 49x - 176.4 \\ \\ 49x + 54y = - 176.4 + 113.4 \\ \\ 49x + 54y = - 63 \\ \\ 49x + 54y + 63 = 0 \\\end{gathered}$

Final answer:

Equation of line is

$\begin{gathered}\bold{\red{49x + 54y + 63 = 0}} \\\end{gathered}$

or

$\begin{gathered}\bold{\green{4.9x + 5.4y + 6.3 = 0 }}\\\end{gathered}$

Answer 2

Answer:

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