Solve y-8=-5/4left(x+10right)

$$y-8=- \frac{ 5 }{ 4 } \left( x+10 \right)$$

Solve for x

$$x=\frac{-4y-18}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{5}{4} by x+10.

$$y-8=-\frac{5}{4}x-\frac{25}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{5}{4}x-\frac{25}{2}=y-8$$

Add \frac{25}{2} to both sides.

$$-\frac{5}{4}x=y-8+\frac{25}{2}$$

Add -8 and \frac{25}{2} to get \frac{9}{2}.

$$-\frac{5}{4}x=y+\frac{9}{2}$$

Divide both sides of the equation by -\frac{5}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{5}{4}x}{-\frac{5}{4}}=\frac{y+\frac{9}{2}}{-\frac{5}{4}}$$

Dividing by -\frac{5}{4} undoes the multiplication by -\frac{5}{4}.

$$x=\frac{y+\frac{9}{2}}{-\frac{5}{4}}$$

Divide y+\frac{9}{2} by -\frac{5}{4} by multiplying y+\frac{9}{2} by the reciprocal of -\frac{5}{4}.

$$x=\frac{-4y-18}{5}$$

Solve for y

$$y=-\frac{5x}{4}-\frac{9}{2}$$

Solution Steps

Use the distributive property to multiply -\frac{5}{4} by x+10.

$$y-8=-\frac{5}{4}x-\frac{25}{2}$$

Add 8 to both sides.

$$y=-\frac{5}{4}x-\frac{25}{2}+8$$

Add -\frac{25}{2} and 8 to get -\frac{9}{2}.

$$y=-\frac{5}{4}x-\frac{9}{2}$$