Full solution

Q. The equation

8 x-6 y=1

is graphed in the

x y

-plane. What is the slope of the line?

Equation in slope-intercept form: To find the slope of the line, we need to write the equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Isolating y: First, we isolate y on one side of the equation. We'll subtract $8x$ from both sides of the equation $8x - 6y = 1$ . $\newline$ $-6y = -8x + 1$
Solving for y: Next, we divide each term by $-6$ to solve for y. $\newline$ $y = \frac{{-8x + 1}}{{-6}}$
Simplifying the equation: Now, we simplify the equation by dividing each term in the numerator by \(-6＂). $\newline$ y = \left(\frac{ $8$ }{ $6$ }\right)x - \frac{ $1$ }{ $6$ }
Identifying the 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 $2$ . $\newline$ $y = \left(\frac{4}{3}\right)x - \frac{1}{6}$
Identifying the 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 $2$ . $\newline$ $y = \frac{4}{3}x - \frac{1}{6}$ Now that we have the equation in slope-intercept form, we can identify the slope, which is the coefficient of $x$ . $\newline$ The slope of the line is $\frac{4}{3}$ .