Question

What is the equation of the line that passes through the given pair points in slope-intercept form?
a.(2, 5.1) and (−1, −0.5) b. (−2, 3) and (3, −4)

Answer 1

a) The equation of the line is $y=\frac{5.6x}{3} + \frac{4.1}{3}$.

b) The equation of the line is $y=\frac{-7x}{5} +\frac{1}{5}$.

Step-by-step explanation:

a) Given, (x₁ , y₁) = (2, 5.1)    and (x₂ , y₂) = (-1, -0.5)

Equation of line passes through (x₁ , y₁) and (x₂ , y₂),

$y - y_{1} = \frac{(y_{2}-y_{1} )}{(x_{2} -x_{1})}(x -x_{1} )$

Now, plug the values in the formula,

$y-5.1 =\frac{(-0.5-5.1)}{(-1-2)} (x-2)\\=> y - 5.1 = \frac{-5.6}{-3} (x-2)\\=> -3y + 15.3 = -5.6x + 11.2\\=> 3y = 5.6x + 4.1\\=> y = \frac{5.6x}{3} +\frac{4.1}{3}$

Hence, the equation of the line is $y=\frac{5.6x}{3} + \frac{4.1}{3}$.

b) Given, (x₁ , y₁) = (-2, 3) and (x₂ , y₂) = (3, -4)

Equation of line passes through (x₁ , y₁) and (x₂ , y₂),

$y - y_{1} = \frac{(y_{2}-y_{1} )}{(x_{2} -x_{1})}(x -x_{1} )$

Now, plug the values in the formula,

$y-3 = \frac{(-4-3)}{(3-(-2))} (x-(-2))\\=> y - 3 = \frac{-7}{5} (x+2)\\=> 5y - 15 = -7x - 14\\=> 5y = -7x + 1\\=> y = \frac{-7x}{5} +\frac{1}{5}$

Hence, the equation of the line is $y=\frac{-7x}{5} +\frac{1}{5}$.