15. Construct the slope-intercept form equation of the line passing through (-5,23) and (10,-5).Equation:

Answer:15y = -28 x + 205.Step-by-step explanation:Slope intercept  form of equation is y = mx + c where m is slope and c is the y intercept.Now slope of line passing through points (-5, 23) and (10, -5):[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \frac{-5 -23}{10 + 5} = \frac{-28}{15}[/tex]Now equation of line: y = mx + csubstituting the value of m in above expression,[tex]y = -\frac{28}{15} x + c[/tex]Now, since the line is passing through the point (-5, 23) therefore, x = -5 and y = 23. By substituting these values in above equation,[tex]23 = -\frac{28}{15} \times (-5) + c[/tex][tex]23 = \frac{28}{3} + c[/tex][tex]c = 23 - \frac{28}{3} = \frac{69 - 28}{3} = \frac{41}{3}[/tex]So equation of line in slope intercept form:[tex]y = -\frac{28}{15} x + \frac{41}{3}[/tex] Further solving,15y = -28 x + 205.