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!
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