Answer:
[tex]\large\boxed{y-8=-\dfrac{1}{2}(x-1)\to\text{point-slope form}}\\\boxed{y=-\dfrac{1}{2}x+\dfrac{17}{2}\to\text{slope-intercept form}}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-\text{slope}\\b-\text{y-intercept}\\\\\text{Let}\\\\k:y=m_1x+b_1\\l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2\\=========================[/tex]
[tex]\text{We have the equation:}\\\\y=2x+1\\\\\bold{STEP\ 1:}\\\\m=2\\\\\bold{STEP\ 2:}\\\\m=-\dfrac{1}{2}\\\\\bold{STEP\ 3:}\\\\\text{Subtitute the value of the slope and the coordinates of the given point}\\(1,\ 8)\ \text{to the equation in the slope-point form:}\\\\y-y_1=m(x-x_1)\\\\y-8=-\dfrac{1}{2}(x-1)\\\\\text{Convert to the slope-intercept form}\ y=mx+b:[/tex]
[tex]y-8=-\dfrac{1}{2}(x-1)\qquad\text{use the distributive property}\\\\y-8=-\dfrac{1}{2}x+\dfrac{1}{2}\qquad\text{add}\ 8=\dfrac{16}{2}\ \text{to both sides}\\\\y-8+8=-\dfrac{1}{2}x+\dfrac{1}{2}+\dfrac{16}{2}\\\\y=-\dfrac{1}{2}x+\dfrac{17}{2}[/tex]
