Question

What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x + 10 and passes through the point (15, –5)? The equation of the line in slope-intercept form is y =-5/3 x + ____

Answer 1

The y-intercept of the line perpendicular to the line y = 3/5x + 10 and passes through the point (15, -5) is 25. The complete equation of the line is y = -5/3x + 25.

Step-by-step explanation:

To find the y-intercept of the line that is perpendicular to the line y = \(\frac{3}{5}x + 10\) and passes through the point (15, –5), we first need to determine the slope of the perpendicular line. The slope of the given line is \(\frac{3}{5}\), and the slope of any line perpendicular to it will be the negative reciprocal. Therefore, the slope of the perpendicular line is \(-\frac{5}{3}\).

Next, we use the point-slope form of a linear equation to determine the y-intercept. Using the point (15, –5) and the slope \(-\frac{5}{3}\), we can write the point-slope form as:

y + 5 = \(-\frac{5}{3})(x – 15)

Simplifying this equation, we get the slope-intercept form:

y = \(-\frac{5}{3})x + 25

The y-intercept b of this equation is 25.

Hence, the complete equation of the line in slope-intercept form is y = \(-\frac{5}{3})x + 25.

Answer 2

y = 3/5x + 10...slope here is 3/5. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So we need a slope of -5/3

y = mx + b
slope(m) = -5/3
(15,-5)...x = 15 and y = -5
now we sub for b, the y int
-5 = -5/3(15) + b
-5 = -25 + b
-5 + 25 = b
20 = b

so ur perpendicular equation is : y = -5/3x + 20