What is the equation of the line passing through the points (-3,7) and (3,3)

2 answers:

6 0

$\text{Given that,}\\\\(x_1,y_1) = (-3,7)~~ \text{and}~~(x_2,y_2) =(3,3)\\\\\\\text{Slope, }~~ m =\dfrac{y_2-y_1}{x_2 - x_1}= \dfrac{3-7}{3-(-3)} = -\dfrac{4}{3+3} = -\dfrac 46 = -\dfrac 23\\\\\\\text{Equation with given points ,}\\\\y- y_1 = m(x-x_1)\\\\\implies y -7 = -\dfrac 23 (x +3)\\\\\implies y -7= -\dfrac 23 x - 2\\\\\implies y = -\dfrac 23 x -2 +7 \\\\\implies y = -\dfrac 23 x +5\\\\\implies 3y = -2x +15 \\\\\implies 2x +3y = 15$

abruzzese [7]2 years ago

4 0

Answer:

Step-by-step explanation:

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Anni [7]

<h2>Explanation:</h2><h2></h2>

Hello! remember you have to write complete questions in order to get good and exact answers. Here I'll explain this in a general way assuming the following table:

$\begin{array}{cc}x & y\\0 & 0\\1 & 2\\2 & 4\\3 & 6\\4 & 8\\5 & 10\end{array}$

As you can see, x increases in steps of 1 units. So let's check the difference in y:

$\bullet \ \text{From x=0 to x=1} \\ \\ \Delta y=2-0=2 \\ \\ \\ \bullet \ \text{From x=1 to x=2} \\ \\ \Delta y=4-2=2 \\ \\ \\ \bullet \ \text{From x=2 to x=3} \\ \\ \Delta y=6-4=2 \\ \\ \\ \bullet \ \text{From x=3 to x=4} \\ \\ \Delta y=8-6=2 \\ \\ \\ \bullet \ \text{From x=4 to x=5} \\ \\ \Delta y=10-8=2$

So we have a constant difference and we can conclude the table represents a line. Since the line passes through then y is directly proportional to x, so we can write:

$y=kx \\ \\ Where: \\ \\ k \ is \ constant \ of \ proportionality \ or \ the \ slope$