A straight line has its x-intercept and y-intercept as -6 and 4 respectively. Find the equation of the line in the form of ax+by+c=0
4x - 6y + 24 = 0
A straight line has its x-intercept and y-intercept as -6 and 4 respectively. Find the equation of the line in the form of ax+by+c=0. show the working
4x - 6y + 24 = 0
should have been reduced to
2x - 3y + 12 = 0
of course the both did not show how it got that, so its reply is
basically useless.
quick way: the x and y intercept form
x/-6 + y/4 = 1
multiply both sides by -12
2x - 3y = -12
2x - 3y + 12 = 0
To find the equation of a line in the form ax + by + c = 0, we need to determine the values of a, b, and c.
Given that the x-intercept is -6 and the y-intercept is 4, we can use these points to find the equation.
The x-intercept represents the point at which the line intersects the x-axis. At this point, the y-coordinate is 0. So we have a point (-6, 0).
Similarly, the y-intercept represents the point at which the line intersects the y-axis. At this point, the x-coordinate is 0. So we have a point (0, 4).
To find the slope of the line, we can use the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Using the points (-6, 0) and (0, 4):
slope (m) = (4 - 0) / (0 - (-6))
= 4 / 6
= 2/3
Now that we have the slope (m), we can use it along with any point on the line to find the equation.
Let's choose the point (0, 4) as it is easier to work with.
Using the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Substituting the values:
y - 4 = (2/3)(x - 0)
y - 4 = (2/3)x
To convert this equation into the desired form ax + by + c = 0, we can multiply the entire equation by 3 to eliminate the fraction:
3(y - 4) = 2x
3y - 12 = 2x
2x - 3y + 12 = 0
So, the equation of the line in the form of ax + by + c = 0 is 2x - 3y + 12 = 0.