# What is the slope of EF if E is (0,-2) and F is (3, 2.5)

Question
Vectors and spaces
What is the slope of EF if E is (0,-2) and F is (3, 2.5)

2021-02-12
Hi there, we can tackle this problem by using the slope formula, or (y2 - y1)/ (x2 - x1), between two coordinates, and these are ordered as (x1, y1), or E = (0, -2), and (x2, y2), or that F = (3, 2.5). We can then substitute 2.5 for y2, -2 for y1, and then solve the numerator to give us 4.5 since -2 is multiplied by a negative sign, and so, it is a positive number. Now, we can substitute 3 for x2, and 0 for x1, and then we can solve the denominator to give us 3. Finally, we can divide the numerator (4.5), by the denominator (3), and we get our result: the slope is 1.5 for EF. Hope this helps.

### Relevant Questions

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For each problem below, either prove that the mapping is linear or explain why it cannot be linear.
$$\displaystyle{1}.{f{{\left({x}_{{1}},{x}_{{2}}\right)}}}={\left({2}{x}_{{1}}-{x}_{{2}},{3}{x}_{{1}}+{x}_{{2}}\right)}$$
$$\displaystyle{2}.{L}{\left({x},{y},{z}\right)}={\left({x}+{y},{y}+{z},{z}+{5}\right)}$$
$$\displaystyle{3}.{L}{\left({x},{y}\right)}={\left({x}+{y},{0},{x}-{2}{y}\right)}$$
$$\displaystyle{4}.{f{{\left({x},{y}\right)}}}={\left({2}{x}+{y},-{3}{x}+{5}{y}\right)}$$
$$\displaystyle{5}.{f{{\left({x},{y}\right)}}}={\left({x}^{{2}},{x}+{y}\right)}$$
$$\displaystyle{6}.{L}{\left({x},{y}\right)}={\left({x},{x}+{y},-{y}\right)}$$
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When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)
I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)
Part A
What is Q for path abc?
Express your answer to two significant figures and include the appropriate units.
Part B
f Pc=1/2Pb, what is W for path cda?
Express your answer to two significant figures and include the appropriate units.
Part C
What is Q for path cda?
Express your answer to two significant figures and include the appropriate units.
Part D
What is Ua?Uc?
Express your answer to two significant figures and include the appropriate units.
Part E
If Ud?Uc=42J, what is Q for path da?
Express your answer to two significant figures and include the appropriate units.
$$\displaystyle{E}={5.0}\times{10}^{{3}}\frac{{N}}{{C}}$$