Question

a. Graph the line that passes through the points (1, -4) and (-2, 2). b. What are the x- and y-intercept of this line?

Answer 1

To graph the line that passes through two points, we first need to determine the equation of the line.

The equation of the line that passes through two points A and B is expressed as

`\begin{gathered} y-y_1=((y_2-y_1)/(x_2-x_1))(x-x_1)\text{ ------ equation 1} \\ where \\ (x_(1,)y_1)\text{ and \lparen x}_(2,)y_2)\text{ are the coordinates of the points A and B respectively,} \\ through\text{ which the line passes.} \end{gathered}`

Given that the line passes through the points (1, -4) and (-2, 2), this implies

`\begin{gathered} x_1=1 \\ y_1=-4 \\ x_2=-2 \\ y_2=2 \end{gathered}`

Substituting these values into equation 1, we have

Thus, the equation of the line that passes through the points (1, -4) and (-2, 2) is

`y=-2x-2`

To graph the line,

`\begin{gathered} when\text{ x=0, we have} \\ y=-2(0)-2=0-2 \\ \Rightarrow y=-2 \\ when\text{ y=0, we have} \\ 0=-2x-2 \\ add\text{ 2 to both sides of the equation} \\ 0+2=-2x-2+2 \\ \Rightarrow2=-2x \\ divide\text{ both sides by the coefficient of x, which is -2} \\ (2)/(-2)=(-2x)/(-2) \\ \Rightarrow x=-1 \end{gathered}`

Given the points (1, -4), (-2, 2), (0,-2) and (-1,0), the graph of the line is as shown below: