using the point-slope form linear equation, y - 3 = 3 (x +1), what is the equation in standard form of a parallel line that passes through (0,2)? On the parallel line, what is the ordered pair...

using the point-slope form linear equation, y - 3 = 3 (x +1), what is the equation in standard form of a parallel line that passes through (0,2)?

On the parallel line, what is the ordered pair where x = -2?

Will you please show the all the steps for these problems.  Thank u!

Asked on by marley112

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ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

Posted on

First step is to identify the slope of the line with the given equation. The general equation in point-slope form is 

`y-y_0 = m(x - x_0)`

Here, `(x_0, y_0)`

is a point on the line and m is the slope. So, in the given equation, slope is m = 3.

Parallel lines have the same slope, so the line parallel to the line with the given equation has the slope m = 3 as well. Since the line in question passes through the point (0, 2), we can write its equation in point-slope form as

y - 2 = 3(x - 0)

y - 2 = 3x

y = 3x + 2

The general equation in standard form is ax + by = c, where a, b, and c are integers. To convert given equation to standard form, subtract y from both sides and subtract 2 from both sides:

0 = 3x - y + 2

-2 = 3x - y

3x - y = -2.

If x = -2, then y = 3(-2) + 2 = -6 + 2 = -4. The ordered pair (-2, -4) satisfies the equation of the parallel line.

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tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The slope intercept form of a line is y = mx + c where m is the slope and c is the y-intercept.

For the given equation y - 3 = 3 (x +1), the slope intercept form can be obtained as follows:

y - 3 = 3*(x + 1)

y - 3 = 3x + 3

y = 3x + 6

The slope of this line is 3

A line parallel to this line passing through (0, 2) is:

(y - 2)/(x - 0) = 3

y - 2 = 3x

For a point on the line with x-coordinate -2, the y-coordinate is -2*3 + 2 = -4

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