MATH SOLVE

4 months ago

Q:
# what equation represents the line that passes through (-8,11) and (4,7/2)

Accepted Solution

A:

For this case we have that by definition, the equation of the line in slope-intersection form is given by:[tex]y = mx + b[/tex]Where:m: It's the slopeb: It is the cutoff point with the y axisWe have:[tex](x1, y1): (- 8,11)\\(x2, y2): (4,3.5)[/tex][tex]m = \frac {y2-y1} {x2-x1} = \frac {3.5-11} {4 - (- 8)} = \frac {-7.5} {4 + 8} = \frac {-7.5} {12 } = - \frac {\frac {15} {2}} {12} = - \frac {15} {24} = - \frac {5} {8}[/tex]Thus, the equation will be given by:[tex]y = - \frac {5} {8} x + b[/tex]We substitute a point to find "b":[tex]11 = - \frac {5} {8} (- 8) + b\\11 = 5 + b\\b = 11-5\\b = 6[/tex]Finally:[tex]y = - \frac {5} {8} x + 6[/tex]Answer:[tex]y = - \frac {5} {8} x + 6[/tex]