Question

A line passes through (-2, 7) and (3, 2).

Answer 1

$\huge{ \mathfrak{ \underline{ Answer \: \: ✓ }}}$

Slope of the line :

$\large\boxed{ \mathrm{ \frac{y_2 - y_1 }{x_2 - x_1} }}$

• $\dfrac{7 - 2}{ - 2 - 3}$

• $\dfrac{ 5}{ - 5}$

• $- 1$

therefore, m = slope = -1

The equation of the line will be :

• y = mx + b

• y = (-1 × x) + b

• y = -x + b

Now, let's plug the value of x and y from coordinates of second point,

• $y = - x + b$

• $2 = - 3 + b$

• $b = 5$

Hence, the required values are :

• $\boxed{m = - 1}$

• $\boxed{ \: \: \: b = 5 \: \: \: }$

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Answer 2

Answer:

m = - 1

b = 5

Step-by-step explanation:

$slope, m= \frac{2-7}{3--2}= \frac{-5}{5}= -1\\\\equation : (y-y_1)= m(x-x_1)$

             $(y-7) = -1(x--2)\\y-7 = -1(x+2)\\y = -1x-2+7\\y= -1x+5$