+107 Line \(l_1 \) represents the graph of \(3x + 4y = -14\). Line \(l_2\) passes through the point \((-5,7)\), and is perpendicular to line \(l_1\). If line \(l_2\) represents the graph of \(y=mx +b\), then find \(m+b\).
+23246 Step 1: Find the slope of 3x + 4y = -14
4y = -3x - 14
y = (-3/4)x - 14/4
The slope is -3/4
Step 2: Find the slope of the perpendicular line; it will be the negative reciprocal: 4/3
Step 3: Use the point slope form to find the equation: y - y1 = m(x - x1)
y - 7 = (4/3)(x + 5)
Step 4: Write this equation in slope-intercept form:
y - 7 = (4/3)(x + 5)
y - 7 = (4/3)x + 20/3
y = (4/3)x + 41/3
Step 5: Identify m and b.
Step 6: Find m + b.
