Convert the equation $y+5=-2(x-3)$ to general form.
Answer (1)
Distribute the -2 on the right side of the equation: y + 5 = − 2 x + 6 .
Subtract 5 from both sides to isolate y: y = − 2 x + 6 − 5 .
Simplify the equation: y = − 2 x + 1 .
The equation in slope-intercept form is: y = − 2 x + 1 .
Explanation
Understanding the Problem We are given the equation y + 5 = − 2 ( x − 3 ) and asked to convert it to slope-intercept form, which is y = m x + b , where m is the slope and b is the y-intercept.
Distributing the -2 First, we distribute the -2 on the right side of the equation:
y + 5 = − 2 ( x − 3 )
y + 5 = − 2 x + 6
Isolating y Next, we subtract 5 from both sides of the equation to isolate y :
y + 5 − 5 = − 2 x + 6 − 5
y = − 2 x + 1
Final Answer The equation is now in slope-intercept form, y = − 2 x + 1 .
Examples
Understanding slope-intercept form is useful in many real-world scenarios. For example, if you are tracking the cost of a taxi ride, the initial fee could be the y-intercept and the cost per mile could be the slope. Knowing the equation in slope-intercept form allows you to easily calculate the total cost for any distance traveled. Similarly, in physics, understanding linear relationships helps in analyzing motion and forces.
