The x-intercept for the line 2x + 3y + 6 = 0 would be the value of x for which y = 0.
Setting y = 0 in the equation gives:
2x + (3)(0) + 6 = 0
2x + 6 = 0
2x = -6
x = -3
For the line to be parallel to 2x - 5y - 7 = 0, the slope would have to be the same.
The slope is determined by putting this equation in slope-intercept format y = mx + b where m is the slope and b is the y-intercept.
Solving the above equation for y we get:
2x - 5y - 7 = 0
5y = 2x - 7
y = (2/5)x - 7/5
The slope of the line is therefore 2/5
Therefore, the line equation is: y = (2/5)x + b
We can find the y-intercept "b" because we know the x-intercept of the line is at x = -3. Therefore, the line passes through (-3,0)
Plugging in these values for x and y gives:
0 = (2/5)(-3) + b
0 = -6/5 + b
b = 6/5
Therefore, the equation for the line is: y = (2/5)x + 6/5