Question

Please help me with this.

Answer 1

`\large\boxed{y-8=-(1)/(2)(x-1)\to\text{point-slope form}}\\\boxed{y=-(1)/(2)x+(17)/(2)\to\text{slope-intercept form}}`

Explanation:

`\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=-(1)/(m_1)\\\\k\ ||\ l\iff m_1=m_2\\=========================`

`\text{We have the equation:}\\\\y=2x+1\\\\\bold{STEP\ 1:}\\\\m=2\\\\\bold{STEP\ 2:}\\\\m=-(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=-(1)/(2)(x-1)\\\\\text{Convert to the slope-intercept form}\ y=mx+b:`

`y-8=-(1)/(2)(x-1)\qquad\text{use the distributive property}\\\\y-8=-(1)/(2)x+(1)/(2)\qquad\text{add}\ 8=(16)/(2)\ \text{to both sides}\\\\y-8+8=-(1)/(2)x+(1)/(2)+(16)/(2)\\\\y=-(1)/(2)x+(17)/(2)`