Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A line passes through point
(6,7) and has a slope of
(3)/(2). Write an equation in
Ax+By=C form for this line. Use integers for
A,B, and
C.

A line passes through point $(6,7)$ and has a slope of $\frac{3}{2}$ . Write an equation in $A x+B y=C$ form for this line. Use integers for $A, B$ , and $C$ .

View step-by-step help

View step-by-step help

Write a linear equation from a slope and a point

Full solution

Q. A line passes through point

(6,7)

and has a slope of

\frac{3}{2}

. Write an equation in

A x+B y=C

form for this line. Use integers for

A, B

, and

C

.

Identify Equation Form: Identify the slope-intercept form of the equation using the given slope and point. $\newline$ Using $y = mx + b$ , where $m = \frac{3}{2}$ and the point is $(6,7)$ . $\newline$ Substitute into $y = mx + b$ : $\newline$ $7 = \left(\frac{3}{2}\right)(6) + b$ $\newline$ $7 = 9 + b$ $\newline$ $b = 7 - 9$ $\newline$ $b = -2$
Convert to Standard Form: Convert the slope-intercept form to $Ax+By=C$ form. $\newline$ Starting from $y = \frac{3}{2}x - 2$ , rearrange to get rid of the fraction: $\newline$ $2y = 3x - 4$ $\newline$ Now, rearrange to $Ax + By = C$ form: $\newline$ $-3x + 2y = -4$
Adjust Coefficients: Adjust the equation to ensure all coefficients are integers. Multiply the entire equation by $-1$ to make the constants positive: $3x - 2y = 4$

More problems from Write a linear equation from a slope and a point

Question

(0, 4)

satisfy the equation

y = x

?

\newline

Choices: [[yes]][[no]]

Posted 3 months ago

Question

Find the slope of the line

y = -4x + \frac{2}{5}

\newline

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

Posted 2 months ago

Question

Rewrite the following equation in slope-intercept form.

\newline

y + 8 = -8(x - 10)

\newline

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

\newline

Posted 2 months ago

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.

\newline

Posted 2 months 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 2 months 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 2 months 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 2 months 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 3 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 3 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 2 months ago