The equation in slope intercept form is [tex]y=-\frac{3}{2} x-3[/tex]
Explanation:
The given pair of points are [tex](2,-6)[/tex] and [tex](-4,3)[/tex]
The slope can be determined using the formula,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Substituting the points [tex](2,-6)[/tex] and [tex](-4,3)[/tex] in the slope formula, we have,
[tex]m=\frac{3+6}{-4-2}[/tex]
[tex]m=\frac{9}{-6}[/tex]
[tex]m=-\frac{3}{2}[/tex]
The equation in slope intercept form can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting [tex]m=-\frac{3}{2}[/tex] and the point [tex](2,-6)[/tex] in the above formula, we get,
[tex]y+6=-\frac{3}{2} (x-2)[/tex]
[tex]y+6=-\frac{3}{2} x+3[/tex]
[tex]y=-\frac{3}{2} x+3-6[/tex]
[tex]y=-\frac{3}{2} x-3[/tex]
Thus, the equation in slope intercept form is [tex]y=-\frac{3}{2} x-3[/tex]
