Question

What can be concluded about a line that passes through the points (2) and 412 Check all that apply. The slope is 0. The y-intercept is-2. The line is vertical. The line is horizontal. The line has no y-intercept. The equation of the line is y2

Answer 1

We are given that a line passes through the points (1, -2) and (4, -2)

Recall that the equation of the line in slope-intercept form is given by

`y=mx+b`

Where m is the slope and b is the y-intercept.

The slope of the line is given by

`m=(y_2−y_1)/( x_2−x_1)`
`\text{where}(x_1,y_1)=(1,-2)\text{and}(x_2,y_2)=(4,-2)`

Let us substitute the given values into the slope formula

`m=(-2-(-2))/(4-1)=-(-2+2)/(3)=(0)/(3)=0`

So the slope is 0 (check option 1)

Now let us find the y-intercept (b)

Choose any one point from the given two points

Let choose (1, -2) and substitute it into the slope-intercept equation

`\begin{gathered} y=mx+b \\ -2=0\cdot1+b \\ -2=0+b \\ b=-2 \end{gathered}`

So the y-intercept is -2 (check option 2)

The equation of the line becomes

`\begin{gathered} y=mx+b \\ y=0\cdot x-2 \\ y=0-2 \\ y=-2 \end{gathered}`

So the equation of the line is y = -2 (check option 6)

Also note that horizontal lines have 0 slope.

Since the slope is 0, it is a horizontal line (check option 4)

Conclusion:

Options 1, 2, 4 and 6 are correct.