Find the slope of the line graphed below.

Find the slope of the line graphed below.

Answer first: I can’t determine the numeric slope because the graph itself wasn’t attached — please upload the graph image or tell me two clear points on the line (for example (x1,y1) and (x2,y2)). Meanwhile, here is exactly how to find the slope from a graphed line plus worked examples so you can finish this quickly once you give the graph.

Concept

The slope m of a line measures its steepness and is the ratio of the vertical change (“rise”) to the horizontal change (“run”) between any two distinct points on the line:
$$m=\frac{\text{change in }y}{\text{change in }x}=\frac{y_2-y_1}{x_2-x_1}.$$

Steps to find slope from a graph

  1. Identify two points on the line that lie exactly at grid intersections (integer coordinates). Call them $(x_1,y_1)$ and $(x_2,y_2)$. Prefer points far apart to reduce reading error.
  2. Compute the rise: $y_2-y_1$ (can be positive, negative, or zero).
  3. Compute the run: $x_2-x_1$ (can be positive or negative, but do not swap order — keep matching points).
  4. Compute the slope: $$m=\frac{y_2-y_1}{x_2-x_1}.$$ Simplify the fraction; keep the sign.
  5. Interpret the sign: if $m>0$ the line rises left-to-right; if $m<0$ it falls left-to-right; if $m=0$ it’s horizontal; if undefined (division by zero) it’s a vertical line.

Two quick examples

Example A (positive slope):

  • Points: $(1,2)$ and $(4,5)$.
  • Rise: $5-2=3$. Run: $4-1=3$.
  • Slope: $$m=\frac{3}{3}=1.$$

So the line has slope 1 (45° up-right).

Example B (negative slope):

  • Points: $(-2,3)$ and $(2,-1)$.
  • Rise: $-1-3=-4$. Run: $2-(-2)=4$.
  • Slope: $$m=\frac{-4}{4}=-1.$$

So the line falls one unit for every one unit right.

Example C (vertical line):

  • Points: $(3,-2)$ and $(3,5)$: run $=3-3=0$, so slope undefined (vertical line).

Common reading tips

  • Always pick grid intersection points to avoid reading fractional coordinates.
  • If the two points give a fraction like $\frac{2}{4}$ simplify to $\frac{1}{2}$.
  • If you read coordinates in the wrong order you may get the same result as long as you pair consistently (i.e., subtract $y_1$ from $y_2$ and $x_1$ from $x_2$ with the same pairing).

What I need from you to give the exact numeric slope

  • Upload the image of the graphed line, or
  • Tell me two clear points on the line (e.g., (x1,y1) = (0,2) and (3,5)), or
  • Tell me the y-intercept and another point, or describe the rise and run shown on the graph.

Summary: I can’t compute the numeric slope until I see the graph or two points. Upload the graph or give two points and I’ll compute the slope step-by-step and explain the result.

100% (3 rated)

Related

Which of the following statements is true? If more than one statement is true, identify all the statements which are true. [ 1 point for identifying all true statements, ‐ 0 . 5 points for choosing a wrong combination even if some of the statements chosen are true, 0 points for not answering ] ( i ) An all ‐ pass filter passes through all frequencies unchanged, but can change the phase of the signal ( ii ) If the FIR filter coefficients are symmetric, then it has linear phase ( iii ) FIR filter is computationally more efficient than an IIR filter of comparable performance ( iv ) A filter that does not operate in real ‐ time can be non ‐ causal

A game is said to be fair if the expected value (after considering the cost) is 0. This means that in the long run, both the player and the “house” would expect to win nothing. If the value is positive, the game is in your favor. If the value is negative, the game is not in your favor. At a carnival, you pay $1 to choose a card from a standard deck. If you choose a red card, you double your money, but if you pick a black card, you do not get any. (A standard deck of cards has 52 cards. 26 of the cards are red.)

Calculating tax incidence Suppose that the U.S. government decides to charge cola consumers a tax. Before the tax, 10,000 cases of cola were sold every week at a price of $5 per case. After the tax, 3,000 cases of cola are sold every week; consumers pay $8 per case (including the tax), and producers receive $3 per case. 1) The amount of the tax on a case of cola is $??? per case. 2) Of this amount, the burden that falls on consumers is $??? per case, and the burden that falls on producers is ???$ per case. 3) True or False: The effect of the tax on the quantity sold would have been the same as if the tax had been levied on producers. True/ False