Can you give me the answer to this or help me please

Question

What is an equation of the line that passes through the point (3,-4) and is parallel to the line y = 2x + 5

Answer 1

Lines that are parallel to each other have the same slope. The line that you are given is given in slope-[y-]intercept form, meaning that you can easily determine the slope and the y-intercept by simply looking at the equation: y = 2x + 5.

The number in front of the x is 2; it is called the coefficient of x. It is also the slope. Thus, the slope of the line you were given AND of the line that you need to write is 2. This is your first clue to finding the answer you need.

Your second clue is that your answer must be a line that goes through the point (3, –4). This means that, for your line (the answer), if you put 3 in for x and –4 in for y, the equation must be true.

So, we set up a template of an equation of a line in slope-[y-]intercept form. Generically, your equation is y = ax + b. Now, you know what a is, because a is equal to the slope. So, we fill in the value of the slope (a) in the equation, giving us y = 2x + b.

Next, we fill in the values of x and y, using the values from the point you were given, which is (3, –4). Now, you have –4 = 2(3) + b. You solve this equation for the unknown, which is b and which will end up being a constant in your equation of the line. If you do the math, you get –4 = 6 + b. Then, you continue to get –10 = b.

We're almost there. We go back to our template of a line: y = ax + b. This time, we only fill in the value of a (the slope) and b (the constant). So, your equation is y = 2x – 10. You could write this as y = 2x + (–10), but that is not conventional.

Answer 2

y=2x-10 has the same slope making it parallel to y=2x+5 and goes through (3,-4)