Answer:
Please check the explanation.
Step-by-step explanation:
1)
From the graph, taking the two points
(3, -5)
(-3, 5)
The slope between (3, -5) and (-3, 5) will be:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{5-\left(-5\right)}{-3-3}[/tex]
[tex]m=-\frac{5}{3}[/tex]
Therefore, the slope is:
[tex]m=-\frac{5}{3}[/tex]
2)
1ST METHOD
We know that the y-intercept of the graph of the linear function can be determined by setting x=0 and solving for y
- As the graph crosses the y-axis at x=0
From the graph, it is clear that:
at x=0, y=0
Thus, the y-intercept is: (0, 0)
2ND METHOD
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where 'm' is the slope and 'b' is the y-intercept
substituting the point (3, -5) and m=-5/3 in the slope-intercept form
[tex]y=mx+b[/tex]
[tex]-5=\frac{-5}{3}\left(3\right)+b[/tex]
[tex]\frac{-5}{3}\left(3\right)+b=-5[/tex]
[tex]-5+b=-5[/tex]
[tex]b=0[/tex]
Thus, the y-intercept is: (0, 0)
3)
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
substituting m=-5/3 and b=0 to determine the equation line in the slope-intercept form
[tex]y=\frac{-5}{3}x+0[/tex]
Therefore, the equation line in the slope-intercept form is:
[tex]y=\frac{-5}{3}x+0[/tex]
where m=-5/3 and b=0
