Answer:
A. [tex]\displaystyle y = -\frac{1}{2} x -4[/tex]
Step-by-step explanation:
Equation of a Line
The equation of the line in slope-intercept form is:
y=mx+b
Where:
m = slope
b = y-intercept.
The point-slope form of the equation of a line is:
y - k = m ( x - h )
Where:
(h,k) is a point through which the line passes.
The line we are looking for has a slope defined for the fact that is perpendicular to the line shown in the graph.
Two perpendicular lines with slopes m1 and m2 satisfy the equation:
[tex]m_1m_2=-1[/tex]
We'll find the slope m1 of the given line and then solve the above equation for m2:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
The line of the graph passes through two clear points (-3,-3) and (0,3). Let's calculate the slope.
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m_1=\frac{3+3}{0+3}=\frac{6}{3}=2[/tex]
Now we calculate the second slope:
[tex]\displaystyle m_2=-\frac{1}{2}[/tex]
We use the point-slope form, given the point (6,-7):
[tex]\displaystyle y + 7 = -\frac{1}{2} ( x - 6 )[/tex]
Operating the parentheses:
[tex]\displaystyle y + 7 = -\frac{1}{2} x +\frac{1}{2}\cdot 6 )[/tex]
Simplifying:
[tex]\displaystyle y = -\frac{1}{2} x +3-7[/tex]
A. [tex]\mathbf{\displaystyle y = -\frac{1}{2} x -4}[/tex]
