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!
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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.
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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