Find the slope and the y-intercept for the line that passes through (-7,-12) (3,12)

## Find the slope and the y-intercept for the line that passes through (-7,-12) (3,12)

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# 2 Answers

Given the two points on the line (-7, -12) and (3, 12). We can find both the slope and the y-int using the equation of a line

y = mx + b

Step 1:

Find the Slope

m = (y

_{2 }- y_{1}) / (x_{2}- x_{1}) - pick your points (I will say (3, 12) is point 1 and (-7,-12) is point 2)= ((-12) - 12) / ((-7) - 3) = -24/-10

which can be reduced to 12/5

Step 2:

Find y-int

(Using the equation of the line y = mx +b)

- pick a point (I picked (3,12) )
- plug in x,y, and m value

we get... 12 = (12/5)*(3) + b

Lets solve for b

12 - (36/5) = b (subtract (12/5)*3 from both sides to get b alone)

60/5 - 36/5 = b (convert to common denominator by multiplying by 5)

24/5 = b

Now we have the equation of the line

y = m x + b

y = (12/5)x + (24/5)

We know two points on the line: (-7, -12) and (3, 12)

slope = (y

_{2}- y_{1})/(x_{2}- x_{1}) = [12 - (-12)]/[3 - (-7)] = (24/10) = (12/5)So we now know that the equation of the line is

y = (12x/5) + b, where be is the y-intercept

Substituting the values of x and y for one of the points (3, 12) gives

12 = [(12)(3)/(5)] + b

b = 12 - [(12)(3)/(5)] = 12 - (36/5) = [(60 - 36)/5) = (24/5)

y = (12x/5) + (24/5)

Double check:

Does -12 = [(12)(-7)/5] + (24/5)?

Does -12 = (-84/5) + (24/5)?

Does -12 = (-60/5)

**YES!!!**