The general equation of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]
Where the slope m of a line that passes thorugh two points (x_1,y_1) and (x_2,y_2) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Use the coordinates of the points (0,6) and (1,8) to find the slope of the desired line:
[tex]\begin{gathered} m=\frac{8-6}{1-0} \\ =\frac{2}{1} \\ =2 \end{gathered}[/tex]
The y-intercept is the value at which the line crosses the y-axis when x=0. Since the point (0,6) is already being considered, we know that b=6.
Substitute m=2 and b=6 into the equation of a line in slope-intercept form:
[tex]y=2x+6[/tex]
Therefore, y=2x+8 is the equation of a line containing (0,6) and (1,8).
