Question

Line t passes through (4, 5) and is perpendicular to the line shown on the coordinate grid. 6 01 22 X 3 5 What is the equation of linet in standard form?

Answer 1

Explanation

Step 1

find the slope of the given line

Let

P1(0,3)

P2(6,2)

$\text{slope}=\frac{y_2-y_1}{x_2-x_1}$

replace

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_1=\frac{2-3}{6-0}=\frac{-1}{6}=-\frac{1}{6} \end{gathered}$

Step 2

2 lines are perpendicular if

$\begin{gathered} \text{slope}_1\cdot slope_2=-1 \\ \text{replace} \\ -\frac{1}{6}\cdot slope_2=-1 \\ \text{slope}_2=-1\cdot-6 \\ \text{slope}_2=6 \end{gathered}$

so, the line we need to find has slope =6 and passes through the poitn (4,5)

Step 3

finally , find the equation of the line

Let

slope=6

P1(4,5)

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