I need to check and see if this is correct?
1). The first equation that I am using for my discussion is: y=x+4 and the parallel must past through this given point (-7, 1)
y=x=-4 is the equation and (-7, 1) is the ordered pair
y=x+4 Since I want the new line parallel, I need to change the slope
y-y1=m(x-x1) point of slope
y-y1=1(x-(-7) since it must have the same slope, it must look like
y = x + b,
plug in your new point, (-7, 1)
1 = -7 + 1 ---->b = 8
new equation: y = x+8
yes
I did not entirely follow all your steps though.
The way I do it
y = 1 x + 4
m = 1, so my new m must be 1 also if parallel ( I did not follow you here)
point is (-7, 1)
1 = 1(-7) + b
yes b = 8
y = x + 8
where is the origin located in this equation?
The origin is always at (0,0)
However none of your lines go through the origin.
Oh, I see what you are doing.
given
y = x + 4
we want parallel
and through (-7,1)
since y = 1 x + 4
has slope = m = 1
ANY parallel line ALSO has slope = 1
slope = 1 = (y-yp)/(x - x1)
or
1 = ( y - 1 ) / (x - -7)
1 = (y-1) / (x+7)
y-1 = x + 7
y = x + 8
I like my way better, but the slope method works.
typo yp should be y1
How about this equation, does it have an origin and what is an x and y intercept?
2). My second equation that I am using is: y=-1/2x+1, and the perpendicular must pass through this given point (4, 2).
y=1/2+1 equation and (4, 2) is the ordered pair
Slope m=-1/2
So the slope of perpendicular =-1/m=2
y=2x+b put in point
2=2(4) +b Simplify
b=-6
y=2x-6 my answer in slope-intercept form
To check if the equation y = x + 8 is correct for a line parallel to y = x + 4 passing through the point (-7, 1), you can follow these steps:
1. Start with the given equation of the line: y = x + 4.
2. Determine the slope of the given line. In this case, the slope is 1, because the coefficient of x in the equation is 1.
3. Use the point-slope formula to find the equation of the parallel line. The point-slope formula is: y - y1 = m(x - x1), where m represents the slope and (x1, y1) is a point on the line. Plugging in the values for the given point (-7, 1) and the slope 1, we have: y - 1 = 1(x - (-7)).
4. Simplify the equation from step 3. Simplifying the right side gives: y - 1 = x + 7.
5. Rearrange the equation to the standard form y = mx + b. Move the x term to the other side: y = x + 7 + 1. Simplifying, we get: y = x + 8.
Therefore, the equation y = x + 8 is correct for a line parallel to y = x + 4 passing through the point (-7, 1).