Write an equation of the line that passes through the given point and is parallel to the given line.
1 answer:
Answer:
1. Equation of line is y=2x+1
2. Equation of line is y=-4x-7
Step-by-step explanation:
Theory :
Equation of line is given as y = mx + c.
Where, m is slope and c is y intercepted.
1.
Slope of given line : y = 2x-5 is m=2.
We know that line : y = 2x-5 is parallel to equation of target line.
therefore, slope of target line will be 2.
we write equation of target line as y=2x+c
Now, It is given that target line passes through point ( 1,3 ).
hence, point ( 1,3 ) satisfy the target line's equation.
we get,
y=2x+c
3=2 1 + c
3=2+c
c=1
thus, Equation of line is y=2x+1
2.
Slope of given line : y = -4x+3 is m= -4
We know that line : y = -4x+3 is parallel to equation of target line.
therefore, slope of target line will be -4
we write equation of target line as y=-4x+c
Now, It is given that target line passes through point ( -2,1 ).
hence, point ( -2,1 ) satisfy the target line's equation.
we get,
y=-4x+c
1= -4 -2+ c
1=8+c
c=-7
thus, Equation of line is y=-4x-7
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Step-by-step explanation:
When a question asks for the "end behavior" of a function, they just want to know what happens if you trace the direction the function heads in for super low and super high values of x. In other words, they want to know what the graph is looking like as x heads for both positive and negative infinity. This might be sort of hard to visualize, so if you have a graphing utility, use it to double check yourself, but even without a graph, we can answer this question. For any function involving x^3, we know that the "parent graph" looks like the attached image. This is the "basic" look of any x^3 function; however, certain things can change the end behavior. You'll notice that in the attached graph, as x gets really really small, the function goes to negative infinity. As x gets very very big, the function goes to positive infinity.
Now, taking a look at your function, 2x^3 - x, things might change a little. Some things that change the end behavior of a graph include a negative coefficient for x^3, such as -x^3 or -5x^3. This would flip the graph over the y-axis, which would make the end behavior "swap", basically. Your function doesn't have a negative coefficient in front of x^3, so we're okay on that front, and it turns out your function has the same end behavior as the parent function, since no kind of reflection is occurring. I attached the graph of your function as well so you can see it, but what this means is that as x approaches infinity, or as x gets very big, your function also goes to infinity, and as x approaches negative infinity, or as x gets very small, your function goes to negative infinity.
