The slope-intercept form of the line follows the pattern below:
[tex]y=mx+b[/tex]
where m = slope and b = y-intercept.
Based on the question, we already have the slope but not the y-intercept instead, what we have is a slope and a point on the line. With this, let's solve the equation using slope-point form first. The pattern is:
[tex]y-y_1=m(x-x_1)[/tex]
where m = slope still and (x₁, y₁) = the coordinate of the point on the line.
Based on the question, our slope = 1/6 and the point is at (6, 3). Let's plug this in to the slope-point form pattern above.
[tex]y-3=\frac{1}{6}(x-6)[/tex]
Then, solve for y.
[tex]\begin{gathered} \text{Distribute 1/6.} \\ y-3=\frac{1}{6}x-\frac{6}{6} \\ y-3=\frac{1}{6}x-1 \\ \text{Add 3 on both sides of the equation.} \\ y-3+3=\frac{1}{6}x-1+3 \\ y=\frac{1}{6}x+2 \end{gathered}[/tex]
Hence, the equation of the line in slope-intercept form is y = 1/6x + 2 as shown above.
