Answer:
-6x + 7y = 11
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-3, -1) and (1/2, 2). Substitute:
[tex]m=\dfrac{2-(-1)}{\frac{1}{2}-(-3)}=\dfrac{3}{3\frac{1}{2}}=\dfrac{3}{\frac{7}{2}}=3\cdot\dfrac{2}{7}=\dfrac{6}{7}\\\\y-(-1)=\dfrac{6}{7}(x-(-3))\\\\y+1=\dfrac{6}{7}(x+3)}[/tex]
Convert to the standard form Ax + By = C:
[tex]y+1=\dfrac{6}{7}(x+3)[/tex] multiply both sides by 7
[tex]7y+7=6(x+3)[/tex] use the distributive property
[tex]7y+7=6x+18[/tex] subtract 7 from both sides
[tex]7y=6x+11[/tex] subtract 6x from both sides
[tex]-6x+7y=11[/tex]
