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12 votes
12 votes
Find the equation for the line that passes through the points ( 7 , 2 ) and ( 10 , − 6 ) . Give your answer in slope intercept form

User Reginald Blue
by
3.1k points

2 Answers

25 votes
25 votes

Answer:

y =
(-8)/(3)x +
(62)/(3)

Explanation:

Use slope formula.

then substitute slope for m in y = mx + b

pick a set of coordinates and substitute them in for x and y.

Solve for b

User Jackuars
by
2.8k points
27 votes
27 votes

Answer:


y=-(8)/(3)x+(62)/(3)

Explanation:

Hi there!

Slope-intercept form:
y=mx+b where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)


m=(y_2-y_1)/(x_2-x_1) where two given points are
(x_1,y_1) and
(x_2,y_2)

Plug in the points (7,2) and (10,-6)


m=(2-(-6))/(7-10)\\m=(2+6)/(7-10)\\m=(8)/(-3)

Therefore, the slope of the line is
-(8)/(3). Plug this into
y=mx+b:


y=-(8)/(3)x+b

2) Determine the y-intercept (b)


y=-(8)/(3)x+b

Plug in one of the given points and solve for b


2=-(8)/(3)(7)+b\\2=-(56)/(3)+b

Add
(56)/(3) to both sides to isolate b


2+(56)/(3)=-(56)/(3)+b+(56)/(3)\\(62)/(3)=b

Therefore, the y-intercept is
(62)/(3). Plug this back into
y=-(8)/(3)x+b:


y=-(8)/(3)x+(62)/(3)

I hope this helps!