Answer :
This question is based on the intercepts of line.Therefore, the intercepts are, x - intercept[tex]( \dfrac{-29}{5} , 0)[/tex] and y-intercept[tex](0,\dfrac{-29}{3})[/tex].
Given:
The points (–4, –3) and (–1, –8) are on a line.
According to the question,
The intercepts of a graph are the points, at which line meets with the x axis and the y axis.
Now, find the equation of the line.
- Finding slope:
[tex]Slope = \dfrac{Change \; in \; y}{Change \; in \; x} \\\\Slope = \dfrac{y_2 - y_1}{x_2 - x_1} \\\\Slope= \dfrac{-3-(-8)}{-4-(-1)} \\\\Slope= \dfrac{-5}{3}[/tex]
- Finding y-intercept:
We know that equation of line is ,
y = mx + b
[tex]-8 = \dfrac{-5}{3} (-1) +b\\\\b = \dfrac{-29}{3}[/tex]
Therefore, the y - intercept is (0, [tex]\dfrac{-29}{3}[/tex] )
Equation of line become = [tex]y = \dfrac{-5}{3} x -\dfrac{29}{3}[/tex]
- Find the x intercept by plugging 0 in the place of y in the equation.
[tex]0 = \dfrac{-5}{3} x -\dfrac{29}{3} \\\\x = \dfrac{-29}{3} \times \dfrac{-3}{5}\\\\x = \dfrac{29}{5}[/tex]
Thus, the x - intercept is [tex]( \dfrac{-29}{5} , 0)[/tex].
Therefore, the intercepts are, x - intercept[tex]( \dfrac{-29}{5} , 0)[/tex] and y-intercept[tex](0,\dfrac{-29}{3})[/tex].
For further details, please refer this link:
https://brainly.com/question/14180189