Answer: [tex]y=\frac{3}{2}x-1[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Knowing that this line passes through the points (4, 5) and (6, 8), we can find the slope with the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. Then:
[tex]m=\frac{5-8}{4-6}=\frac{3}{2}[/tex]
Substitute one point and the slope into [tex]y=mx+b[/tex] and solve for "b":
[tex]5=\frac{3}{2}(4)+b\\\\5-6=b\\\\b=-1[/tex]
Then, the equation of this line in Slope-Intercept form is:
[tex]y=\frac{3}{2}x-1[/tex]
