Answer:
Question 4: [tex]y=\displaystyle -\frac{4}{5}x[/tex]
Question 5: [tex]y=-5x-3[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept (the y-coordinate of the point where the line crosses the y-axis).
Question 4
1) Determine the slope (m)
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that pass through the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
In the graph, two easy-to-identify points on the line are (-5,4) and (5,-4). Plug these into the equation:
[tex]\displaystyle m=\frac{-4-4}{5-(-5)}\\\\\displaystyle m=\frac{-4-4}{5+5}\\\\\displaystyle m=\frac{-8}{10}\\\\\displaystyle m=-\frac{4}{5}[/tex]
Therefore, the slope of the line is [tex]\displaystyle -\frac{4}{5}[/tex]. Plug this into [tex]y=mx+b[/tex] as the slope (m):
[tex]y=\displaystyle -\frac{4}{5}x+b[/tex]
2) Determine the y-intercept (b)
On the graph, we can see that the line crosses the y-axis when y is 0. Therefore, the y-intercept (b) is 0. Plug this into [tex]y=\displaystyle -\frac{4}{5}x+b[/tex]:
[tex]y=\displaystyle -\frac{4}{5}x+0\\\\y=\displaystyle -\frac{4}{5}x[/tex]
Question 5
1) Determine the slope (m)
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Two easy-to-identify points are (-1,2) and (0,-3). Plug these into the equation:
[tex]\displaystyle m=\frac{-3-2}{0-(-1)}\\\\\displaystyle m=\frac{-3-2}{0+1}\\\\\displaystyle m=\frac{-5}{1}\\\\m=-5[/tex]
Therefore, the slope is -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
2) Determine the y-intercept (b)
On the graph, we can see that the line crosses the y-axis at the point (0,-3). The y-coordinate of this point is -3. Therefore, the y-intercept (b) is -3. Plug this into [tex]y=-5x+b[/tex]:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
I hope this helps!
