Question

Which equation represents the line that passes through the points (3-,7) and (3,3)?

Answer 1

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

Answer 2

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