Graph the line that satisfies each set of conditions.

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

The slope of the line passing through the points $\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$ is expressed below.

$m=\frac{y_2-y_1}{x_2-x_1}$

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 $\left(4,1\right)$and perpendicular to graph of $2x+3y=1$.

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

Rewrite the equation in slope intercept form.

Therefore, the slope of the line is evaluated below.

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 $\left(4,1\right)$ move 3 units up (on y-axis) and 2 units right (on x-axis).

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

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