5r + 15 = 0 ........?
2 answers:
You might be interested in
2 Answers:
- B) The lines are parallel
- C) The lines have the same slope.
Parallel lines always have equal slope, but different y intercepts.
==========================================================
Explanation:
Let's solve the second equation for y
3y - x = -7
3y = -7+x
3y = x-7
y = (x-7)/3
y = x/3 - 7/3
y = (1/3)x - 7/3
The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.
However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.
Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.
Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.
I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.
Answer:
For this case m represent the slope and is given by and from the other condition given we know that
. And replacing we got:
And if we reorganize the terms we have:
And subtracting 3 in both sides we got:
Step-by-step explanation:
For this case we have the following function y=g(x) and we want to find the tangent line to this function using the conditions:
So we need a function like this one:
For this case m represent the slope and is given by and from the other condition given we know that
. And replacing we got:
And if we reorganize the terms we have:
And subtracting 3 in both sides we got: