Question

Write an equation for the line parallel to the given line that contains C. C(-3,8); y = 4/5x+5 (Write in slope intercept form)

Answer 1

In the equation you want to find, the constant on the right (the y-intercept) will be the one that lets the line go through the given point. Putting that point in the equation, we can solve for the intercept:

... 8 = (4/5)(-3) + b

Adding 2.4 to each side gives

... 10.4 = b

Your equation is ...

... y = (4/5)x + 10.4

_____

The constant 10.4 could be written 52/5 if you like.

Answer 2

The equation for the line parallel to the given line  y = 4/5x+5 that contains the point C(-3,8) is y = 4/5x + 52/5

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Given that a line is parallel to the line y = 4/5x + 5 and contains the point C(-3, 8). The slope of this line parallel has the same slope a that of y = 4/5x+5

Therefore the slope of the parallel line is 4/5.

Therefore since the line passes through the point C(-3, 8). The equation is given by:

$y-y_1=m(x-x_1)\\\\y-8=\frac{4}{5}(x-(-3))\\\\y-8=\frac{4}{5} (x+3)\\\\y=\frac{4}{5}x+\frac{52}{5}$