Question

Write the equation of the line in slope-intercept form if possible: thru the point (2,-9) perpendicular to the line 10/3y-5x= -2

Answer 1

First, let's figure out the slope of the given line by writing the given line in slope-intercept form.

`(10)/(3)y - 5x = -2 \\ \\ (10)/(3)y = 5x - 2 \\ \\ y = (3)/(10)(5x - 2) \\ \\ y = (3)/(2)x - (3)/(5)`

For a line in slope-intercept form, the coefficient of x is the slope of the line. The slope of the given line is 3/2.

You want a line perpendicular to the given line. Slopes of perpendicular lines are opposite recipricals. That means the numerator and denominator are flipped and the sign is changed.

The slope of a line perpendicular to the given line is -2/3.

You have the slope of -2/3 and also the given point (2, -9). To write the equation of the perpendicular line in slope-intercept form, you need the value of b. You can substitute these values into the formula for slope intercept form to find b, the y-intercept.
y = mx + b
-9 = (-2/3)(2) + b
b = -23/3

The equation of the line that goes through (2, 9) and is perpendicular to (10/3)y - 5x = -2 is y = (-2/3)x - 23/3