Write an equation of the line parallel to Line AB that contains point C.
Line AB: y = -5x + 12; C(-2, 1)
a line with slope m containing (h,k) is
y-k = m(x-h)
Now plug in your values.
can you show me how to do this step by step please?
I just did! The line AB has slope -5.
So, any line parallel AB also has slope -5.
The line you want is thus
y-1 = -5(x+2)
ok thanks you so much!
Well, if you want a line parallel to Line AB, we know that its slope must be the same as Line AB's slope. So, we can start by finding the slope of Line AB, which is -5. Now we will use point-slope form to write the equation of the line:
m = -5 (slope of Line AB)
C(-2,1) (coordinates of point C)
y - y1 = m(x - x1)
Here, (x1, y1) represents the coordinates of point C, which are (-2, 1). Plugging in these values, we get:
y - 1 = -5(x - (-2))
Simplifying:
y - 1 = -5(x + 2)
Expanding:
y - 1 = -5x - 10
Finally, let's rewrite that in a more familiar way:
y = -5x - 9
And there you have it – an equation of the line parallel to Line AB that contains point C, C(-2,1). Just remember, it's important to sprinkle a little humor along the way to keep things fun!
To find the equation of the line parallel to line AB that contains point C, we need to first determine the slope of line AB. The equation of line AB is given as y = -5x + 12, where -5 is the slope of this line.
Since the slope of parallel lines is the same, the slope of the line we are looking for will also be -5.
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given as:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope.
Using the point C(-2, 1) and the slope -5, we can substitute the values into the point-slope form to get the equation:
y - 1 = -5(x - (-2))
Simplifying further:
y - 1 = -5(x + 2)
y - 1 = -5x - 10
Rearranging the equation to the standard form:
5x + y = -9
Therefore, the equation of the line parallel to line AB that contains point C is 5x + y = -9.