Question

X intercept is 1 and (-1, -4) find the equation of the line when given two points from the line.

Answer 1

Answer: y=2x-2

Explanation:

X intercept is 1

Hence,

(1,0)

Thus,

(1,0) (-1.-4)

Equation of a straight line:

`\displaystyle\\\boxed {(x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1) }`

x₁=1 x₂=-1 y₁=0 y₂=-4

`\displaystyle\\(x-1)/(-1-1) =(y-0)/(-4-0) \\\\(x-1)/(-2) =(y)/(-4) \\\\`

Multiply both parts of the equation by -4:

(2)(x-1)=y

2x-2=y

Answer 2

`y=2x-2`

Explanation:

The x-intercept is when the line crosses the x-axis, so when y = 0.

Therefore, the two points on the line are:

• (1, 0)
• (-1, -4)

To find the equation of the line when given two points from the line, first find the slope:

`\textsf{slope}\:(m)=\frac{\textsf{change in $y$}}{\textsf{change in $x$}}=(-4-0)/(-1-1)=2`

Now substitute the found slope and one of the points (1, 0) into the point-slope form of a linear equation:

`\implies y-y_1=m(x-x_1)`

`\implies y-0=2(x-1)`

`\implies y=2x-2`

Therefore, the equation of the line is:

`y=2x-2`