Writing the Equation of a Line given the Graph
Answer:
15. [tex]y = \underline{16x}[/tex]
16. [tex]y = \underline{15x}[/tex]
Step-by-step explanation:
We can write our line in Slope-Intercept form, [tex]y = mx +b[/tex], where [tex]b[/tex] is the [tex]y[/tex]-intercept of the line which is the [tex]y[/tex]-coordinate when [tex]x = 0[/tex]and [tex]m[/tex] is the slope of the line which is calculated by [tex]\frac{y_2 -y_1}{x_2 -x_1}\\[/tex] where [tex]x_n[/tex] and [tex]y_n[/tex] is the [tex]xy[/tex]-coordinates of any point [tex]n[/tex] on the line.
For problem 15, we can see that at [tex]x = 0[/tex], [tex]y = 0[/tex] as well. So [tex]b = 0[/tex]. To calculate the slope of the line, we choose any two points that is on line. We can see that points [tex](0,0)[/tex] and [tex](2,32)[/tex] is on the line so these are our points [tex]1[/tex] and [tex]2[/tex].
Calculating the slope:
[tex]m = \frac{32 -0}{2 -0} \\ m = \frac{32}{2} \\ m = 16[/tex]
Now we can plug everything we know and it is [tex]y = 16x +0[/tex] or [tex]y = 16x[/tex].
We can apply the same procedure for problem 16. At [tex]x = 0[/tex], [tex]y = 0[/tex] so [tex]b = 0[/tex]. For the slope, we can choose the points, [tex](2,30)[/tex] and [tex](4,60)[/tex].
I'm not choosing [tex](0,0)[/tex] (although choosing it will make it easier) just for kicks but the bottom line is, you can choose any point on the line you want.
Calculating the slope:
[tex]m = \frac{60 -30}{4 -2} \\ m = \frac{30}{2} \\ m = 15[/tex]
The equation of the line can be written as [tex]y = 15x[/tex].
