Respuesta :
Answer:
[tex]y=\frac{1}{2}x+2[/tex]
Step-by-step explanation:
We can find the slope by using the formula
[tex]\text{slope}=\frac{y_1-y_2}{x_1-x_2}[/tex].
Plugging in the points (2,3) and (6,5), we have
[tex]\text{slope}=\frac{5-3}{6-2}=\frac{2}{4}=\frac{1}{2}.[/tex]
Therefore, the slope is [tex]\frac{1}{2}.[/tex] We can then write the line in slope-intercept form, which is [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
We already found the slope, so we know the equation is of the form
[tex]y=\frac{1}{2}x+b.[/tex]
We can now plug in either one of the points to find [tex]b.[/tex] Plugging in (2,3), we get
[tex]3=\frac{1}{2}(2)+b[/tex].
To solve for [tex]b[/tex], we can subtract 1 from both sides of the equation:
[tex]3=1+b[/tex]
[tex]b=3-1=2[/tex].
Now, we have all the variables we need to write the equation in slope-intercept form. We know [tex]m=\frac{1}{2}[/tex] and [tex]b=2[/tex], so the equation is
[tex]y=\frac{1}{2}x+2.[/tex]
