Question

The graph of line g passes through the points (6, -2) and (-2, 2). Which of the following statements is true?

A The slope of the line is -2.
B The zero of line g is 1.
C The point (-8, 4) lies on g.
D The -intercept is 1

Answer 1

D) The y-intercept is 1.

Explanation:

To determine which of the given statements about line g are true, we first need to find the equation of line g.

To find the slope (m) of line g, given that it passes through the points (6, -2) and (-2, 2), substitute these points into the slope formula:

`m=(y_2-y_1)/(x_2-x_1)=(2-(-2))/(-2-6)=(4)/(-8)=-(1)/(2)`

Therefore, the slope of the line is m = -1/2.

Substitute the calculated slope and one of the given points into the point-slope formula. Then, rearrange the equation to its slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept:

`\begin{aligned}y-y_1 &=m(x-x_1)\\\\y-(-2) &=-(1)/(2)(x-6)\\\\y+2 &=-(1)/(2)x+3\\\\y &=-(1)/(2)x+1\end{aligned}`

So the equation of line g is:

`y=-(1)/(2)x+1`

Therefore, the slope of the line is -1/2 and the y-intercept is 1.

To find the zero (x-intercept) of the line, substitute y = 0 into the equation of the line and solve for x:

`\begin{aligned}-(1)/(2)x+1&=0\\\\-(1)/(2)x&=-1\\\\x&=2\end{aligned}`

Therefore, the zero of line g is 2.

Finally, to verify whether the point (-8, 4) lies on line g, substitute x = -8 into the equation and check if y equals 4:

`\begin{aligned}y&=-(1)/(2)(-8)+1\\\\y&=4+1\\\\y&=5\end{aligned}`

Since y does not equal 4, we can conclude that the point (-8, 4) does not lie on line g.

Therefore, the only true statement is:

• D) The y-intercept is 1.

Answer 2

D. The y-intercept is 1

Explanation:

Slope:

The slope of a line is calculated by finding the change in the y-coordinate divided by the change in the x-coordinate.

Slope = (y2 - y1) / (x2 - x1)

In this case, the slope is:

Slope = (2 - (-2)) / (-2 - 6) = 4 / -8 = -1/2

Therefore, statement A is False.

Zero:

The zero of a line is the x-coordinate of the point where the line crosses the x-axis.

To find the zero of the line, we can set the y-coordinate equal to 0 and solve for x.

y = mx + b

0 = (1/2)x + b

-b = (1/2)x

b = -(1/2)x

Therefore, the zero of the line is not equal to 1.

Point:

We can check whether the point (-8, 4) lies on the line by substituting the x- and y-coordinates into the equation of the line.

y = mx + b

4 = -(1/2)(-8) + b

4 = 4 + b

b = 4 - 4

b = 0

Therefore, the line equation is:

y = -(1/2)x

Substituting the x-coordinate of the point (-8, 4) into the equation, we get:

4 = -(1/2)(-8)

4 = 4

Since the y-coordinate of the point is equal to the value of the line equation at that point, statement C is false.

Intercept:

The y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis.

To find the y-intercept, we can solve (-2,2) in the equation, we get

y = mx + b

2 = -(1/2)(-2) + b

b = 2 -1

b = 1

Therefore, the y-intercept of the line is equal to 1 .

Therefore, statement D is true.

Conclusion:

Correct answer is:

D The y-intercept is 1