Q34.

Graph the line that satisfies each set of conditions.

34. passes through $(4, 1)$ , perpendicular to graph of $2 x + 3 y = 1$

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Answer

The graph of the line is provided below.

1Step-1 – Apply the concept of slope

The slope of the line passing through the points $(x_{1}, y_{1}) and (x_{2}, y_{2})$ is expressed below.

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

2Step-2 –Compute the intercept

The y-intercept of a graph is when the x-coordinate is 0. The point where the graph of the equation cuts the y-axis.

It is provided that line passes through the point $(4, 1)$ and perpendicular to graph of $2 x + 3 y = 1$ .

Product of slopes of perpendicular lines is $- 1$ . This means slope of line is $- 1$ divided by slope of the line $2 x + 3 y = 1$ .

Rewrite the equation in slope intercept form.

\begin{matrix} 2 x + 3 y - 2 x = 1 - 2 x \\ 3 y = 1 - 2 x \\ y = \frac{1}{3} - \frac{2}{3} x \\ y = - \frac{2}{3} x + \frac{1}{3} \end{matrix}

Therefore, the slope of the line is evaluated below.

\begin{matrix} m = - \frac{1}{- \frac{2}{3}} \\ = \frac{3}{2} \end{matrix}

To obtain the other ordered pair through which the line passes interpret the slope. The slope is positive this means the line rises to the right.

Now, from the ordered pair $(4, 1)$ move 3 units up (on y-axis) and 2 units right (on x-axis).

Therefore, the obtained ordered pair is $(6, 4)$ .

3Step-3 – Graph the line

Plot the obtained ordered pairs $(4, 1)$ and $(6, 4)$ on Cartesian plane to obtain the graph of the line with slope $m = \frac{3}{2}$ .