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The equation
8x-6y=1 is graphed in the
xy-plane. What is the slope of the line?

The equation $8 x-6 y=1$ is graphed in the $x y$ -plane. What is the slope of the line?

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Evaluate variable expressions: word problems

Full solution

Q. The equation

8 x-6 y=1

is graphed in the

x y

-plane. What is the slope of the line?

Isolate y-term: To find the slope of the line represented by the equation $8x - 6y = 1$ , we need to solve for $y$ in terms of $x$ to get the equation into slope-intercept form, which is $y = mx + b$ , where $m$ is the slope.
Divide by $-6$ : First, we isolate the $y$ -term on one side of the equation. We can do this by subtracting $8x$ from both sides of the equation. $\newline$ $8x - 6y - 8x = 1 - 8x$ $\newline$ This simplifies to: $\newline$ $-6y = -8x + 1$
Simplify equation: Next, we divide every term by $-6$ to solve for $y$ . $y = \frac{{-8x + 1}}{{-6}}$
Simplify fraction: Now, we simplify the equation by dividing each term on the right side by $-6$ . $\newline$ $y = \left(\frac{8}{6}\right)x - \frac{1}{6}$
Identify slope: We can simplify the fraction $\frac{8}{6}$ to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $y = \left(\frac{4}{3}\right)x - \frac{1}{6}$
Identify slope: We can simplify the fraction $\frac{8}{6}$ to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $y = \frac{4}{3}x - \frac{1}{6}$ The equation is now in slope-intercept form, and the coefficient of $x$ is the slope of the line. So, the slope of the line is $\frac{4}{3}$ .

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