Question

8+ 6+ 3+ 2+ 1+ 1 2 3 4 5 6 7 8 9 -9-8-7-6-5-4-3-2 2 이 -3 4 -5+ TY -6+ -7- Pro -8

Answer 1

To find the equation of the line in its slope-intercept form, you can take two points through which the line passes, find the slope of the line, and then use the point-slope formula.

For example, you can take the points (0,5) and (6,3).

The formula to find the slope of the line is

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ \text{ Where m is the slope of the line and } \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}`

So, you have

`\begin{gathered} (x_1,y_1)=(0,5) \\ (x_2,y_2)=(6,3) \\ m=(3-5)/(6-0) \\ m=(-2)/(6) \\ m=-(1)/(3) \end{gathered}`

Now using the point-slope formula you have

`\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-(1)/(3)(x-0) \\ y-5=-(1)/(3)x \\ \text{ Add 5 from both sides of the equation} \\ y-5+5=-(1)/(3)x+5 \\ y=-(1)/(3)x+5 \end{gathered}`

The equation of a line in its slope-intercept form is

`\begin{gathered} y=mx+b \\ \text{ Where m is the slope of the line and} \\ b\text{ is the y-intercept} \end{gathered}`

Therefore, the equation of the line shown in the graph, in its slope-intercept form is

`y=-(1)/(3)x+5`