Question

find the equation of a line(-6,7) and whose x-intercept is 5.

Answer 1

Answer:

7 x + 11 y - 35 = 0

Step-by-step explanation:

Equation of a line is given by the formula :

y = m x + c where c is the x - intercept .

Equation can also be of the form :

y - y₁ = m ( x - x₁ )

Note that m = ( y₂ - y₁ ) / ( x₂ - x₁ )

We have been told that the x-intercept is 5 .

So the point will be ( 5 , 0 ) as it has an x-intercept of 5 .

From this , we can calculate the slope of the line :

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

x₁ = - 6

x₂ = 5

y₁ = 7

y₂ = 0

= > m = ( 0 - 7 ) / ( 5 - (-6 ) )

= > m = - 7 / 11

So y - y₁ = m ( x - x₁ )

Put x₁ as - 6 and y₁ as 7 :

= > y - 7 = ( - 7 / 11 ) ( x + 6 )

= > 11 y - 77 = - 7 ( x + 6 )

= > 11 y - 77 = - 7 x - 42

= > 7 x + 11 y - 35 = 0

This is the required equation.

Answer 2

To find the equation of line:
point given = (-6,7)
x-intercept = 5

formula: mx + c = y
To find another point, we know the x-intercept which is 5. Therefore (5,0)

m = y2 - y1 / x2 - x1
= 7 - 0 / -6 - 5
= 7 / -11

Substituting:
-7/11 (x) + c = y ..........however (x,y) = (5,0)
-7/11 (5) + c = 0
-35/11 = -c
35/11 = c

therefore,
y = -7/11x + 35/11