Which equation represents the line that passes through the points (3-,7) and (3,3)?A) y = 2/3 x + 1


B) y = -2/3 x + 9


C) y = 2/3 x + 9


D) y = - 2/3 x + 5


Answer:

Did you mean (-3, 7) for the first point??  If so, the answer is

D) y = -2/3x + 5

Step-by-step explanation:

Find the slope: (m)

3-7 / 3+3 = -4/6=-2/3=m

Find the y intercept (b): (plug in y, x, and m)

3=-2/3(3) +b

3=-2+b

5=b

Write equation using y=mx+b

y = -2/3x+5


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The slope-intercept form:

y=mx+b

m - slope

b - y-intercept

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (-3, 7) and (3, 3). Substitute:

m=\dfrac{3-7}{3-(-3)}=\dfrac{-4}{6}=-\dfrac{2}{3}

y=-\dfrac{2}{3}x+b

Put the coordinates of the point (3, 3) to the equation of a line:

3=-\dfrac{2}{3}(3)+b

3=-2+b      add 2 to both sides

5=b\to b=5

Answer: \boxed{y=-\dfrac{2}{3}x+5}\to\boxed{D)}


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