Question

If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of is . If the coordinates of point D are (5 , 5), the equation of line is y = x + .

Answer 1

Answer with explanation:

Equation of line Passing through two points (a,b) and (c,d) is given by:

         $\frac{y-b}{x-a}=\frac{d-b}{c-a}$

Equation of line Passing through two points (8,0) and (3,7) is given by:

      $\rightarrow \frac{y-7}{x-3}=\frac{7-0}{3-8}\\\\\rightarrow \frac{y-7}{x-3}=\frac{7}{-5}\\\\\rightarrow -5 y+35=7 x - 21\\\\\rightarrow 5 y= -7 x +35 +21\\\\ y=\frac{-7 x}{5}+\frac{56}{5}\\\\y=-1.4 x +11.2$

Comparing with slope intercept form of line,

y= m x+c, where , m is slope and c is y intercept.

⇒Y intercept = 11.2

Equation of line Passing through two points (5,5) and (3,7) is given by:

            $\rightarrow \frac{y-7}{x-3}=\frac{7-5}{3-5}\\\\y-7= -1 \times (x-3)\\\\y=7-x+3\\\\y=-x +10$

Comparing with slope intercept form of line,

y= m x+c, where , m is slope and c is y intercept.

⇒Y intercept = 10

Equation of line is, y= -x +10.