Answer:
[tex]y=-\frac{3}{4}x+\frac{1}{2}[/tex]
Step-by-step explanation:
A general equation for a line in the slope-intercept form is y = mx + b.
Given the points (-6, 5) and (-2, 2), we can substitute the first point in the equation:
[tex]\begin{gathered} 5=-6m+b \\ 5+6m=b \\ b=5+6m \end{gathered}[/tex]
Now, we can substitute the second point in the equation and use the relation for "b" found above:
[tex]\begin{gathered} y=mx+(5+6m) \\ 2=-2m+5+6m \\ 2-5=4m \\ -3=4m \\ m=-\frac{3}{4} \end{gathered}[/tex]
Since b = 5 + 6m, we can now find b:
[tex]\begin{gathered} b=5+6\cdot(-\frac{3}{4}) \\ b=5-\frac{18}{4} \\ b=\frac{4\cdot5-18}{4}=\frac{20-18}{4} \\ b=\frac{2}{4}=\frac{1}{2} \end{gathered}[/tex]
Thus, the equation of the line is:
[tex]y=-\frac{3}{4}x+\frac{1}{2}[/tex]
