Question

This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane.
xxx yyy
-79−79minus, 79 -68−68minus, 68
-68−68minus, 68 -51−51minus, 51
-57−57minus, 57 -34−34minus, 34
What is the xxx-intercept of the line?

Answer 1

Answer:

The x-intercept of the line is (-85 , 0)

Step-by-step explanation:

• To find the x-intercept (x at y = 0) of the line find the equation of the line and substitute y by 0

• The form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept (y at x = 0)

• The formula of the slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ The line passes through points (-79 , -68) , (-68 , -51) , (-57 , -34)

- Chose any two points of them to find m

∵ $x_{1}$ = -79 and $y_{1}$ = -68

∵ $x_{2}$ = -68 and $y_{2}$ = -51

∴ $m=\frac{-51--68}{-68--79}=\frac{-51+68}{-68+79}=\frac{17}{11}$

∴ m = $\frac{17}{11}$

Substitute the value of m in the form of the equation

∵ y = $\frac{17}{11}$ x + b

- To find b substitute x and y in the equation by the coordinates

    of any point on the line  

∵ x = -57 and y = -34

∴ -34 =  $\frac{17}{11}$ (-57) + b

∴ -34 =  $\frac{-969}{11}$ + b

- Add $\frac{969}{11}$  to both sides

∴ $\frac{595}{11}$ = b

∴ y = $\frac{17}{11}$ x +  $\frac{595}{11}$

Substitute y by 0 to find x-intercept

∵ y = 0

∴ 0 = $\frac{17}{11}$ x +  $\frac{595}{11}$

- Multiply both sides by 11

∴ 0 = 17 x + 595

- Subtract 595 from both sides

∴ -595 = 17 x

- Divide both sides by 17

∴ -85 = x

∴ The x-intercept of the line is (-85 , 0)

Answer 2

Answer:

(-35, 0)

step-by-step explanation: