Question

Complete the point-slope equation of the line through (1,-1) and (5,2)
Use exact numbers
Y-(1,-1)=

Answer 1

The point-slope form is $y=\frac{3}{4} x-\frac{7}{4}.$

Solution:

Given points are (1, –1) and (5, 2).

Let us first find the slope of the equation.

$m=\frac{y_2-y_1}{x_2-x_1}$

⇒ $m=\frac{2-(-1)}{5-1}$

⇒ $m=\frac{2+1}{4}$

⇒ $m=\frac{3}{4}$

Equation of a line in point-slope form is $y-y_1=m(x-x_1)$.

Substitute any one point (1, –1) and $m=\frac{3}{4}$ in the point-slope formula

⇒ $y-(-1)=\frac{3}{4} (x-1)$

⇒ $y+1=\frac{3}{4} (x-1)$

Cross multiply the fraction.

⇒ $4(y+1)=3(x-1)$

⇒ $4y+4=3x-3$

⇒ $4y=3x-7$

⇒ $y=\frac{3}{4} x-\frac{7}{4}$

Hence, the point slope form is $y=\frac{3}{4} x-\frac{7}{4}.$