# Find the equation of the line which has Y-intercept 4 &is parallel to line 2x-3y=7.Find the co-ordinates of the point where it cuts X-axis.

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Expert Answers

justaguide | Certified Educator

The equation of a line with a y-intercept of c and a slope of m is given as y=mx + c.

The line we have to determine is parallel to the line 2x - 3y = 7. This is possible if they have the same slope.

2x - 3y = 7

=> 3y = 2x - 7

=> y = (2/3)x - (7/3)

The slope of the line we have to determine is (2/3). Its y-intercept is 4, this gives the equation of the line as

y = (2/3)x + 4

=> 3y = 2x + 12

=> 2x - 3y + 12 = 0

Where the line intersects the x-axis y = 0

=> 2x = -12

=> x = -6

The coordinates of the point where it intersect the x- axis is (-6 , 0)

**The required equation of the line is 2x - 3y + 12 = 0 and the coordinates of the point where it intersects the x-axis are (-6 , 0)**