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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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Standard form: find x- and y-intercepts

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 $\frac{4}{3}$ .

More problems from Standard form: find x- and y-intercepts

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satisfy the equation

y = x

?

\newline

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Question

Rewrite the following equation in slope-intercept form.

\newline

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Write your answer using integers, proper fractions, and improper fractions in simplest form.

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Question

y

-intercept of the line

14x - 16y = -10

\newline

Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

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Posted 1 month ago

Question

q

\frac{-2}{3}

r

is perpendicular to

q

. What is the slope of line

r

\newline

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

\newline

\_\_\_\_\_

Posted 1 month ago

Question

Find the slope of the line

y + 3 = -\frac{1}{18}(x + 6)

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

p

has an equation of

y = -8x + 6

q

, which is perpendicular to line

p

, includes the point

(2, -2)

. What is the equation of line

q

?

\newline

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

\newline

Posted 1 month ago

Question

Is the graph of this equation a horizontal or vertical line?

\newline

x = 7

\newline

\newline

\text{(A)horizontal line}

\newline

\text{(B)vertical line}

Posted 2 months ago

Question

Rewrite the following equation in standard form.

\newline

y = -10x + 7

\newline

Hint: The standard form of a linear equation is

\newline

Ax + By = C

A

B

are not both zero, and

A

B

C

are integers whose GCF is

1

Posted 2 months ago

Question

A line with a slope of

9

passes through the point

(9,9)

. What is its equation in point-slope form?

\newline

Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

\newline

y - \underline{\hspace{1cm}} = \underline{\hspace{1cm}} (x - \underline{\hspace{1cm}})

Posted 1 month ago