Question 1147615
formula for line j is y = 2x + 8
line k is perpendicular to line j.
it will therefore have a slope that is a negative reciprocal to the slope of line j.
the general formula for line k is therefore y = -1/2 * x + b
since line k passes through the point (6,-6), then use that point to find the value of b.
replace x with 6 and y with -6 in the equation of y = -1/2 * x + b to get:
-6 = -1/2 * 6 + b
simplify to get:
-6 = -3 + b
solve for b to get:
b = -6 + 3 = -3
the equation of line k is therefore y = -1/2 * x - 3
here's the graph.you can see that the point (6,-6) is on that line, as well as see that the lines do indeed look perpendicular to each other.
<img src = "http://theo.x10hosting.com/2019/102502.jpg" alt="$$$" >
line j is the red line.
line k is the blue line.
y-intercept for line j is 8, as it should be.
y-intercept for line k is -3, as it should be.
intersection of line j and k is at the point (-4.4,-.8)
line k passes through the point (6,-6), as it should.