Write an equation in slope-intercept form of the line satisfying the given conditions.
Through (-7,15), perpendicular to 4x + 9 y = 44
First, we need to find the slope of the line 4x + 9y = 44. We can rearrange this equation into slope-intercept form, y = mx + b, where m is the slope. To do this, we need to isolate y:
4x + 9y = 44
9y = -4x + 44
y = (-4/9)x + 44/9
The slope of this line is -4/9.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. So, the slope of the line perpendicular to 4x + 9y = 44 is the negative reciprocal of -4/9, which is 9/4.
Now we have the slope (m) and a point (-7, 15). We can substitute these values into the slope-intercept form equation, y = mx + b, to find the y-intercept (b).
15 = (9/4)(-7) + b
15 = -63/4 + b
To solve for b, we can add 63/4 to both sides:
15 + 63/4 = b
(60 + 63)/4 = b
123/4 = b
So the y-intercept is 123/4.
Putting it all together, the equation of the line, in slope-intercept form, that is perpendicular to 4x + 9y = 44 and passes through (-7, 15) is y = (9/4)x + 123/4.