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.

Identify Equation Form: Identify the slope-intercept form of the equation using the given slope and point. Using y = mx + b, where m = 3/2 and the point is (6,7). Substitute into y = mx + b: 7 = (3/2)(6) + b 7 = 9 + b b = 7 - 9 b = -2 Convert to Standard Form: Convert the slope-intercept form to Ax+By=C form. Starting from y = (3/2)x - 2, rearrange to get rid of the fraction: 2y = 3x - 4 Now, rearrange to Ax + By = C form: -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

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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 $C$ .

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Math Problems

Grade 8

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: $3x - 2y = 4$