The line which joins the point A(3,k) and B(-2,5) is parallel to the line whose equation is 5y+2x-7=0.Find the value of k
A line that is parallel to 5y+2x-7=0 has the same slope. To find the slope of this line, we can write it in slope-intercept form:
5y+2x-7 = 0
5y = -2x + 7
y = (-2/5)x + 7/5
The slope of this line is -2/5. Since the line that joins A(3,k) and B(-2,5) is parallel to this line, it must also have a slope of -2/5. We can use the formula for the slope of a line between two points:
slope = (y2-y1)/(x2-x1)
where (x1,y1) and (x2,y2) are the coordinates of the two points. Since we know the slope and one of the points (B(-2,5)), we can solve for the other point:
-2/5 = (k-5)/(3-(-2))
-2/5 = (k-5)/5
-2 = k-5
k = 3
Therefore, the value of k is 3.