Answer:
y= ⅗x +1
Explanation:
Given line: y= ⅗x +4
Gradient= ⅗
The gradient of the line can be found from the coefficient of x. This applies only when the equation is in the slope-intercept form (y= mx +c).
In the slope-intercept form, the coefficient of y is 1 and all the other terms and constant is on the right-hand side of the equation while the y term is on the left-hand side.
Parallel lines have the same gradient. Thus the line parallel to y= ⅗x +4 would have the equation of y= ⅗x +c, where c is the y-intercept.
To find the value of c, substitute a pair of coordinates into the equation.
Given that the line passes through (-5, -2), we can substitute this coordinates into y= ⅗x +c.
When x= -5, y= -2,
-2= ⅗(-5) +c
-2= -3 +c
c= -2 +3
c= 1
Thus, the equation of the line is y= ⅗x +1.