Answer:
- The equation of the line is:
[tex]y=\frac{1}{2}x+5[/tex]
Step-by-step explanation:
Considering the line graph
Some of the points on the line are given by
Finding the slop between any two given points
Let us take the point (0, 5) and (2, 6)
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:5\right),\:\left(x_2,\:y_2\right)=\left(2,\:6\right)[/tex]
[tex]m=\frac{6-5}{2-0}[/tex]
To the y-intercept, set x = 0.
We already know that when x = 0, the value of y = 5
so
Equation of line can be obtained using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 1/2 and any point let say (2, 6)
[tex]y-6=\frac{1}{2}\left(x-2\right)[/tex]
add 6 to both sides
[tex]y-6+6=\frac{1}{2}\left(x-2\right)+6[/tex]
[tex]y=\frac{1}{2}x+5[/tex]
Therefore, the equation of the line is:
- [tex]y=\frac{1}{2}x+5[/tex]
