Having trouble solving this...
Write the equation if a line that goes through (6,-1/2) and has an x-intercept of 5x-2y=-20
I think the x-intercept is -4, but I don't know what to do with that.
Hmmm. The phrase "an x-intercept of 5x-2y=-20" doesn't mean anything. The x-intercept is a point, not an equation.
you are correct that the given line has an x-intercept of -4, and if you want your new line to have the same intercept, then just draw the line through (6,-1/2) and (-4,0).
Otherwise, you may need to re-examine the problem.
Your wording makes no sense.
Did you mean that the new line has the same x-intercept as 5x-2y= -20 ?
since the x-intercept is indeed -4, I will assume that the question is as I assumed.
So we have two points on the new line
(6, -1/2) and (-4,0)
slope = (0-1/2)/(-4-6) = -1/20
equation must be
x + 20y = c
with (-4,0) on it
-4 + 0 = c
c = -4
equation: x + 20y = -4
or
y = (-1/20)x - 1/5
To write the equation of a line, you need two things: the slope of the line and a point it passes through. In this case, you are given a point (6, -1/2) and the x-intercept of another line in the form of an equation, 5x - 2y = -20.
To find the slope of the line, you can rearrange the given equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. To do this, solve the equation for y:
5x - 2y = -20
-2y = -5x - 20
y = (5/2)x + 10
From the equation above, we can see that the slope of the line is 5/2.
Now that we have the slope, we can use the point-slope formula to write the equation of the line. The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Using the point (6, -1/2) and the slope of 5/2, we can substitute the values into the formula:
y - (-1/2) = (5/2)(x - 6)
Simplifying:
y + 1/2 = 5/2x - 15/2
To get rid of the fractions, we can multiply every term by 2:
2y + 1 = 5x - 15
Finally, rearrange the equation to have y on one side:
2y = 5x - 16
And there you have it! The equation of the line that passes through the point (6, -1/2) and has the x-intercept of 5x - 2y = -20 is 2y = 5x - 16.