Question

Find the equation of the straight line parallel to th line passing through the points (1,3) and (4,6).​

Answer 1

Step-by-step explanation:

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Answer 2

Given,

A line passes through the points (1, 3) and (4, 6).

To find,

Equation of the line parallel to the given line.

Solution,

When two lines are parallel then, the slopes of both lines are equal. So to find the equation of a line parallel to the line passing through (1, 3) and (4, 6), we need to know the slope.

Now, the slope of a line passing through 2 points $(x_1,x_2) \hspace{3} and \hspace{3} (y_1,y_2)$ is given by,

$m=\frac{y_2-y_1}{x_2-x_1}$

Here, the given line passes through (1, 3) and (4, 6). So,

$m=\frac{6-3}{4-1}$

⇒ $m=\frac{3}{3}$

⇒ m = 1.

So the line parallel to this line must also have slope = m = 1.

Now, the slope-intercept form of a line is

$y=mx+c$

Where m = slope, and c = y-intercept.

So the equation of a line when m = 1, will be

$y = x+c$

c being the y-intercept.

There shall be different equations of the lines when we put different values of c that is, y-intercept.

Therefore, the equation of the straight line parallel to the line passing through the points (1,3) and (4,6), will be (y = x + c).