Question

Find an equation of the line that passes through the point (3, 4) and is perpendicular to the line 2x - 5y = -3.

Answer 1

Convert the equation from standard form to slope-intercept form.

2x - 5y = -3

Solve for y.

2x - 5y = -3

-5y = -3 - 2x

y = 3/5 + 2/5x

y = 2/5x + 3/5

The slope of a perpendicular line is the reciprocal and opposite of the orginal line.

2/5 -> -5/2

Equation of the perpendicular line:

y = -5/2x + 3/5

Now, we need to find a point that passes through the point (3, 4).

On a graph, we can keep adjusting the y-intercept till we get that makes the line pass through the given point. We get 11.5 or 23/2

Or we can solve the given point

y = -5/2x + b

4 = -5/2(3) + b

4 = -15/2 + b

23/2 = b

Therefore, the answer is y = -5/2x + 23/2

Best of Luck!

Answer 2

$\text{Hello there! :)}$

$\large\boxed{y = -\frac{5}{2}x + \frac{23}{2}}$

$\text{Begin by rewriting the given equation into slope-intercept form:}\\\\2x - 5y = -3\\\\-5y = -2x - 3\\\\y = \frac{2}{5}x + \frac{3}{5}\\\\\text{A perpendicular line has a slope of the opposite reciprocal, therefore:}\\\\\frac{2}{5} \text{ becomes } \frac{-5}{2} \\\\\text{Substitute slope, y-coordinate and x-coordinate into slope-intercept formula:}\\\\4 = \frac{-5}{2}(3) + b\\ \\4 = -\frac{15}{2} + b\\\\\frac{8}{2} = -\frac{15}{2}+ b\\\\\frac{23}{2} = b$

$\\\text{Write the final equation:}\\\\y = -\frac{5}{2}x + \frac{23}{2}$