In order to find the line equation, first consider that you can write the general equation of a line as follow:
y - yo = m(x - xo)
where m is the slope and (xo,yo) is any point on the line.
Calculate the slope m by using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are any points on the line.
In this case, you have:
(x1,y1) = (2,5)
(x2,y2) = (6,21)
Replace the previous values of the parameters into the formula for m:
[tex]m=\frac{21-5}{6-2}=\frac{16}{4}=4[/tex]Now, use (xo,yo) = (2,5) and the previous value of m into the general equation for a line, and then solve for y, as follow:
[tex]\begin{gathered} y-5=4(x-2) \\ y-5=4x-8 \\ y=4x-8+5 \\ y=4x-3 \end{gathered}[/tex]The previous result is the required equation in slope-intercept form.
