math

The slope-intercept equation for the line that passes through (-12,10) and is perpendicular to 4x+6y =3 is: 6y = -4x - 54. This can be determined by noting that for two lines to be perpendicular, their slopes must be the negative reciprocal of each other. To calculate the slope of the line that passes through (-12,10) and is perpendicular to 4x+6y =3, the slope of 4x+6y =3 must first be determined. The slope of the line 4x+6y =3 is -4/6, so the slope of the line that passes through (-12,10) and is perpendicular to 4x+6y =3 would be 6/-4 which is the same as -6/4. The slope-intercept form of the equation is y = (-1/6)x - (9). To find the y-intercept, the point-slope form of the equation (y - y1 = m(x - x1)) can be used with the given point (-12,10). The equation becomes y - 10 = (-1/6)(x - (-12)), which can be rearranged as 6y = -4x - 54.