Find the Rate of Change in Linear Equation -8y+2x=6

Q: Why can't I just use the coefficient of x from the original equation?

The coefficient of x in standard form (like -8y + 2x = 6) is NOT the slope! You must first convert to slope-intercept form (y = mx + b) where m is the rate of change.

Q: What's the difference between rate of change and slope?

They're the same thing! Rate of change, slope, and the coefficient of x in y = mx + b all describe how steep the line is and which direction it goes.

Q: How do I remember to isolate y first?

Think of it as "getting y by itself" - just like solving any equation! Move everything else to the right side, then divide by y's coefficient.

Q: What if the coefficient of y is positive instead of negative?

The process is identical! Whether it's 8y + 2x = 6 or -8y + 2x = 6, just isolate y by moving terms and dividing.

Linear Equations with Slope-Intercept Form

For the following straight line equation, state what is the rate of change?

$-8y+2x=6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the slope of the graph

00:05 Arrange the equation to match the linear equation

00:09 Isolate Y

00:29 Arrange the equation

00:33 Write the coefficient multiplier of X

00:37 The coefficient of X is the slope of the graph, which is the rate of change

00:42 Divide by 2

00:45 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

For the following straight line equation, state what is the rate of change?

$-8y+2x=6$

Step-by-step solution

To determine the rate of change for the given equation $-8y + 2x = 6$ , follow these steps:

Step 1: Rearrange the equation to isolate $y$ . Start by subtracting $2x$ from both sides:
$-8y = -2x + 6$ .
Step 2: Solve for $y$ by dividing every term by $-8$ to get $y$ by itself:
$y = \frac{-2}{-8}x + \frac{6}{-8}$ .
Step 3: Simplify the fractions:
$y = \frac{1}{4}x - \frac{3}{4}$ .

In the equation $y = \frac{1}{4}x - \frac{3}{4}$ , the coefficient of $x$ is $\frac{1}{4}$ , which represents the rate of change (slope) of the line. Therefore, the rate of change is $\frac{1}{4}$ .

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rate of Change: The coefficient of x equals the slope
Technique: Solve for y: -8y = -2x + 6 becomes $y = \frac{1}{4}x - \frac{3}{4}$
Check: Coefficient of x in slope-intercept form gives rate of change $\frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Reading rate of change directly from standard form
Don't assume the coefficient of x in -8y + 2x = 6 is the rate of change = wrong answer 2! Standard form coefficients don't directly show slope. Always convert to slope-intercept form y = mx + b first.

Practice Quiz

Test your knowledge with interactive questions

Look at the graph below and determine whether the function's rate of change is constant or not:

FAQ

Everything you need to know about this question

Why can't I just use the coefficient of x from the original equation?

The coefficient of x in standard form (like -8y + 2x = 6) is NOT the slope! You must first convert to slope-intercept form (y = mx + b) where m is the rate of change.

What's the difference between rate of change and slope?

They're the same thing! Rate of change, slope, and the coefficient of x in y = mx + b all describe how steep the line is and which direction it goes.

How do I remember to isolate y first?

Think of it as "getting y by itself" - just like solving any equation! Move everything else to the right side, then divide by y's coefficient.

What if the coefficient of y is positive instead of negative?

The process is identical! Whether it's 8y + 2x = 6 or -8y + 2x = 6, just isolate y by moving terms and dividing.

Why is my answer a fraction when the original numbers were whole?

That's completely normal! When you divide 2 by 8 (or -2 by -8), you get $\frac{1}{4}$ . Many linear equations have fractional slopes.

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