- #1
Joe_1234
- 25
- 0
Find the equation of the line which forms with the axes in the second quadrant a triangle of area 4 and whose intercepts differ by 5.
Last edited by a moderator:
Joe_1234 said:Find the equation of the line which forms with the axes in the second quadrant a triangle of area 4 and whose intercepts differ by 5.
Thank you sirMarkFL said:Let's follow up...we have:
\(\displaystyle ab=-8\implies b=-\frac{8}{a}\)
And so:
\(\displaystyle \left(a+\frac{8}{a}\right)^2=5^2\)
\(\displaystyle \frac{a^2+8}{a}=\pm5\)
\(\displaystyle a^2\pm5a+8=0\)
\(\displaystyle a=\frac{\pm5\pm\sqrt{5^2-32}}{2}\)
And since the discriminant is negative, we find there is no real solution.
A line in the second quadrant is a line that lies entirely in the second quadrant of a coordinate plane. This means that both the x-coordinate and y-coordinate of every point on the line are negative.
To graph a line in the second quadrant, plot points that have negative x and y coordinates and connect them with a straight line. Alternatively, you can find the x and y intercepts of the line and plot those points to create the graph.
The slope of a line in the second quadrant is negative. This means that as you move from left to right along the line, the y-coordinate decreases while the x-coordinate increases.
To find the equation of a line in the second quadrant, you can use the point-slope form (y - y1) = m(x - x1), where m is the slope and (x1, y1) is any point on the line. Alternatively, you can use the slope-intercept form y = mx + b, where b is the y-intercept of the line.
A line in the second quadrant can represent a decrease in temperature over time, a decrease in the value of a stock over time, or a decrease in the number of hours of daylight during the winter season. It can also represent the path of a ball thrown downward, or the trajectory of a plane descending for landing.