graphing standard

Question

passes through the y intercept of the line with the equation 2x+3y=15 and is perpendicular to the line with the equation 3x-4y=12

Answer 1

y = -4x/3 +5 is the line with y intercept = 5 and slope perpendicular to given line in slope intercept form

or

4x +3y = 15 in standard form (ax+by=c, with a=4, b=3, c=15)

Answer 2

We find the y-intercept of 2x + 3y = 15 by letting x = 0 in that equation, and then solving for y. This gives 3y = 15, or y = 5. A handy way to find the equations of lines perpendicular to a given line is to reverse the x- and y-coefficients and simultaneously change the sign of one of them. Thus, a line perpendicular to ax + by = c is bx - ay = d. Doing this to 3x - 4y = 12 produces 4x + 3y = d. To find d, we use the fact that the line has a y-intercept of (0,5), so that 3*5 = d, or d = 15. Hence, the equation of the desired line is 4x + 3y = 15.