Question

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Answer 1

Question:

On a coordinate plane, a line goes through (negative 3, 2) and (0, 1). A point is at (3, 4). What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)? y = –One-thirdx + 5 y = –One-thirdx + 3 y = 3x + 2 y = 3x − 5

Answer:

Option D: $y=3x-5$ is the equation of the line

Explanation:

It is given that the line passes through the points $(-3,2)$ and $(0,1)$

We shall find the equation of the line that passes through the points $(-3,2)$ and $(0,1)$

Slope $m=\frac{1-2}{0+3}$

          $m=\frac{-1}{3}$

Also, it is given that the line is perpendicular to the line having slope $m=\frac{-1}{3}$

Since, we know that if two lines are perpendicular, then the product of the two slope is equal to -1.

Thus, we have,

$m_1\cdot m_2=-1$

$\frac{-1}{3} \cdot m_2=-1$

      $m_2=3$

Thus, the slope of the line is $m=3$ and passes through the point $(3,4)$

Now, we shall find the equation of the line using the formula,

$y-y_1=m(x-x_1)$

Thus, we have,

$y-4=3(x-3)$

$y-4=3x-9$

     $y=3x-5$

Thus, the equation of the line is $y=3x-5$

Hence, Option D is the correct answer.

Answer 2

Answer (D) y=3x-5

Step-by-step explanation: