Straight line mx equals 5y plus 4 has same gradient as line 7x plus 6y plus 5 Find value of m?

mx = 5y + 4

7x + 6y + 5 = 0

If they have the same slope, then we know that Δy/Δx in the first line is equal to Δy/Δx in the second one. Let's solve the second equation for y then:

y = (5 + 7x) / -6
∴y = (-7/6)x - 5/6

So we know it's slope is -7/6. Now let's rearrange our other line appropriately:

y = (m/5)x - 4/5
So the slope of our second line is m/5, which we know is the same as the slope of our other line, -7/6. We can say then that:

m/5 = -7/6
∴m = -35/6 = -55/6 ≈ -5.8333...