For this case we have that by definition, the equation of a line in the slope-intercept form is given by:
[tex]y = mx + b[/tex]
Where:
m: Is the slope
b: Is the cut-off point with the y axis
We have the following equation:
[tex]3x-5y + 10 = 0[/tex]
We manipulate algebraically:
We subtract 10 from both sides of the equation:
[tex]3x-5y = -10[/tex]
We subtract 3x from both sides of the equation:
[tex]-5y = -3x-10[/tex]
We multiply by -1 on both sides of the equation:
[tex]5y = 3x + 10[/tex]
We divide between 5 on both sides of the equation:
[tex]y = \frac {3} {5} x + \frac {10} {5}\\y = \frac {3} {5} x + 2[/tex]
Thus, the equation in the slope-intercept form is [tex]y = \frac {3} {5} x + 2[/tex]
Answer:
[tex]y = \frac {3} {5} x + 2[/tex]
