-8x – 5y =30
The Correct Answer and Explanation is:
To solve the linear equation −8x−5y=30-8x – 5y = 30−8x−5y=30, we can follow these steps:
Step 1: Rearrange the equation to solve for yyy
Let’s start by isolating yyy in the equation. First, we need to get rid of the −8x-8x−8x term on the left-hand side. To do this, we can add 8x8x8x to both sides:−8x−5y+8x=30+8x-8x – 5y + 8x = 30 + 8x−8x−5y+8x=30+8x−5y=8x+30-5y = 8x + 30−5y=8x+30
Step 2: Solve for yyy
Now, to solve for yyy, we need to divide both sides of the equation by −5-5−5:y=8x+30−5y = \frac{8x + 30}{-5}y=−58x+30
Step 3: Simplify the expression
Next, simplify the right-hand side. We can distribute the −5-5−5 into the terms in the numerator:y=8x−5+30−5y = \frac{8x}{-5} + \frac{30}{-5}y=−58x+−530y=−8×5−6y = -\frac{8x}{5} – 6y=−58x−6
Thus, the equation in slope-intercept form is:y=−85x−6y = -\frac{8}{5}x – 6y=−58x−6
Explanation:
The equation −8x−5y=30-8x – 5y = 30−8x−5y=30 is a linear equation, and it can be rewritten in slope-intercept form, which is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.
From the final equation y=−85x−6y = -\frac{8}{5}x – 6y=−58x−6, we can observe that:
- The slope mmm is −85-\frac{8}{5}−58. This means that for every 5 units you move to the right along the x-axis, the value of yyy will decrease by 8 units.
- The y-intercept bbb is −6-6−6, which means the line crosses the y-axis at the point (0,−6)(0, -6)(0,−6).
This equation gives us a straight line where the relationship between xxx and yyy is linear, and you can graph it by plotting the y-intercept and using the slope to find other points.
