Question

Write the slope-intercept form of the equation that passes through the point (2, 3) and is perpendicular to the line y = 5/8x - 4

Answer 1

`\large\boxed{y=-(8)/(5)x+(31)/(5)}`

Explanation:

`\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept`

`\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2\\\\--------------------------`

`\text{We have:}\\\\y=(5)/(8)x-4\to m_1=(5)/(8)\\\\\text{The slope of a perpendicular line:}\ m_2=-(1)/((5)/(8))=-(8)/(5)\\\\\text{The equation:}\\\\y=-(8)/(5)x+b\\\\\text{Put the coordinates of the point (2, 3) to the equation:}\\\\3=-(8)/(5)(2)+b\qquad\text{solve for}\ b\\\\3=-(16)/(5)+b\qquad\text{add}\ (16)/(5)\ \text{to both sides}\\\\(15)/(5)+(16)/(5)=b\to b=(31)/(3)\\\\\text{Finally:}\\\\y=-(8)/(5)x+(31)/(5)`