Question

Bonus: Write the equation of a line in slope intercept form that is parallelto y=4/3x-7 and contains the point (5,-8)

Answer 1

The given equation is

`y=(4)/(3)x-7`

The slope of the given line is 4/3 because it's the coefficient of x.

Now, the new line has a slope of 4/3 too because parallel lines have equal slopes.

We know that the new line passes through the point (5, -8). Let's use the point-slope formula to find the equation.

`y-y_1=m(x-x_1)`

Replacing the points and the slope, we have.

`\begin{gathered} y-(-8)=(4)/(3)(x-5) \\ y+8=(4)/(3)x-(20)/(3) \\ y=(4)/(3)x-(20)/(3)-8 \\ y=(4)/(3)x+(-20-24)/(3) \\ y=(4)/(3)x-(44)/(3) \end{gathered}`

Therefore, the equation of the new line is y = (4/3)x - (44/3).