Question

Find the X- and Y- intercepts of the line that passes through the given points (-4, -4), (8, -1)the x intercept isthe y intercept is

Answer 1

To determine the y- and x- intercepts of the line that passes through the points (-4,-4) and (8,-1) you have to determine the equation of the line first. To do so, you have to use the point-slope form:

$y-y_1=m(x-x_1)$

Where

m represents the slope of the line

(x₁,y₁) represent the coordinates of one of the points of the line

The first step is to calculate the slope of the line, using the formula:

$m=\frac{y_1-y_2}{x_1-x_2}$

Where

(x₁,y₁) represent the coordinates of one of the points of the line

(x₂,y₂) represent the coordinates of a second point of the line

Using

(8,-1) as (x₁,y₁)

(-4,-4) as (x₂,y₂)

You can calculate the slope as follows:

$\begin{gathered} m=\frac{-1-(-4)}{8-(-4)} \\ m=\frac{-1+4}{8+4} \\ m=\frac{3}{12} \\ m=\frac{1}{4} \end{gathered}$

The slope of the line is m=1/4

Next, using the slope and one of the points, for example, point (8,-1) you can determine the equation of the line as follows:

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=\frac{1}{4}(x-8) \\ y+1=\frac{1}{4}(x-8) \end{gathered}$

-distribute the multiplication on the parentheses term

$\begin{gathered} y+1=\frac{1}{4}\cdot x+\frac{1}{4}\cdot(-8) \\ y+1=\frac{1}{4}x-2 \end{gathered}$

-pass +1 to the right side of the equation by applying the opposite operation to both sides of it

$\begin{gathered} y+1-1=\frac{1}{4}x-2-1 \\ y=\frac{1}{4}x-3 \end{gathered}$

The y-intercept is the point where the line crosses the y-axis, at this point the value of x is zero. So replace the equation of the line with x=0 and calculate the corresponding value of y:

$\begin{gathered} y=\frac{1}{4}x-3 \\ y=\frac{1}{4}\cdot0-3 \\ y=-3 \end{gathered}$

The coordinates of the y-intercept are (0,-3)

The x-intercept is the point where the line crosses the x-axis. At this point, the y-coordinate is zero. To determine the coordinates of the x-intercept you have to replace the equation of the line with y=0 and calculate the corresponding value of x:

$\begin{gathered} y=\frac{1}{4}x-3 \\ 0=\frac{1}{4}x-3 \end{gathered}$

-Pass "-3" to the left side of the equation by applying the opposite operation to both sides of it:

$\begin{gathered} 0+3=\frac{1}{4}x-3+3 \\ 3=\frac{1}{4}x \end{gathered}$

-Multiply both sides by 4 to determine the value of x

$\begin{gathered} 3\cdot4=4\cdot\frac{1}{4}x \\ 12=x \end{gathered}$

The coordinates of the x-intercept are (12,0)