Question

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

Answer 1

Step-by-step explanation:

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 $(x_1,y_1)$ is given by

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

here point is (-3.6,2.1)

So,

$y-2.1=m(x+3.6)$

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

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

Slope (m)= -49/54

Put the value of slope in eq1

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

Final answer:

Equation of line is

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

or

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

Hope it helps you.

To learn more:

To obtain the conditions for consistency of a pair of Linear Equations in Two Variables by graphical method. A.2x – y +1...

https://brainly.in/question/43531308

Answer 2

Answer:

y = -4.9/5.4x - 1.17

Step-by-step explanation:

First let's convert the equation to standard form of y = mx + b.

4.9x + 5.4y = 3

Subtract 4.9x from both sides.

5.4y = -4.9x + 3

Divide each term by 5.4.

y = -4.9/5.4x + 0.56

If two lines are parallel to each other, they have the same slope slopes.

The first line is y = -4.9/5.4x + 0.56. Its slope is -4.9/5.4. A line parallel/perpendicular to this one will also have a slope of -4.9/5.4.

Plug this value (-4.9/5.4) into your standard point-slope equation of y = mx + b.

y = -4.9/5.4x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-3.6, 2.1).

Plug in the x and y values into the x and y of the standard equation.

2.1 = -4.9/5.4(-3.6) + b

To find b, multiply the slope and the input of x (-3.6)

2.1 = 3.27 + b

Now, subtract 3.27 from both sides to isolate b.

-1.17 = b

Plug this into your standard equation.

y = -4.9/5.4x - 1.17

This equation is parallel/perpendicular to your given equation (y = -4.9/5.4x + 0.56) and contains point (-3.6, 2.1)

Hope this helps!