Answer :
Question 1.
Given the point:
(-3, -4)
Slope, m = - 1/2
Let's write the equation of the line that passes through the given point with the slope in point-slope form and slope intercept form.
• Point slope form:
Apply the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex]Now substitute -1/2 for m, then input (-3, -4) for x1 and y1 in the equation above.
[tex]\begin{gathered} y-(-4)=-\frac{1}{2}(x-(-3)) \\ \\ y+4=-\frac{1}{2}(x+3) \end{gathered}[/tex]Therefore, the equation in point slope form is:
[tex]y+4=-\frac{1}{2}(x+3)[/tex]• SLope intercept form:
Apply the slope intercept form of a linear equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Substitute the following:
-1/2 for m
(-3, -4) for (x, y)
Then solve for b.
[tex]\begin{gathered} -4=-\frac{1}{2}(-3)+b \\ \\ -4=\frac{3}{2}+b \\ \\ \end{gathered}[/tex]Subtract 3/2 from both sides:
[tex]\begin{gathered} -4-\frac{3}{2}=\frac{3}{2}-\frac{3}{2}+b \\ \\ -\frac{4}{1}-\frac{3}{2}=b \\ \\ \frac{-8-3}{2}=b \\ \\ -\frac{11}{2}=b \\ \\ b=-\frac{11}{2} \end{gathered}[/tex]Therefore, the slope intercept form of the line is:
[tex]y=-\frac{1}{2}x-\frac{11}{2}[/tex]ANSWER:
Point-slope form:
[tex]y+4=-\frac{1}{2}(x+3)[/tex]Slope intercept form:
[tex]y=-\frac{1}{2}x-\frac{11}{2}[/tex]