The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have the point (6, -7) and the slope m = -3/2. Substitute:
[tex]y-(-7)=-\dfrac{3}{2}(x-6)\\\\\boxed{y+7=-\dfrac{3}{2}(x-6)}[/tex]
[tex]y+7=-\dfrac{3}{2}(x-6)[/tex] use distributive property
[tex]y+7=-\dfrac{3}{2}x+9[/tex] subtract 7 from both sides
[tex]\boxed{y=-\dfrac{3}{2}x+2}[/tex]
[tex]y=-\dfrac{3}{2}x+2[/tex] multiply both sides by 2
[tex]2y=-3x+4[/tex] add 3x to both sides
[tex]\boxed{3x+2y=4}[/tex]
Answer:
point-slope form: [tex]y+7=-\dfrac{3}{2}(x-6)[/tex]
slope-intercept form: [tex]y=-\dfrac{3}{2}x+2[/tex]
standard form: [tex]3x+2y=4[/tex]
