Question

Which linear equation in two variables has a graph that passes through the points (3, –5) and (–7, 13)?

A. y - 3 = -9/5(x + 5)
B. y + 5= -9/5(x - 3)
C.y – 13 = -9/2(x + 5)
D. y – 5 = -9/2(x + 3)

Answer 1

Answer:

Option B. $y+5=-\frac{9}{5}(x-3)$

Step-by-step explanation:

step 1

Find the slope m

we have the points

$(3, -5)\ and\ (-7, 13)$

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{13+5}{-7-3}$

$m=\frac{18}{-10}$

Simplify

$m=-\frac{9}{5}$

step 2

Find the equation of the line in point slope form

we know that

The linear equation in point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=-\frac{9}{5}$

$(x1,y1)=(3,-5)$

substitute

$y-(-5)=-\frac{9}{5}(x-3)$

$y+5=-\frac{9}{5}(x-3)$