Question

Find an equation of the line passing through the pair of points. Write the equation in the form Ax + By = C.
left parenthesis 4 comma 7 right parenthesis and left parenthesis 3 comma 4 right parenthesis(4,7) and (3,4)
The equation of the line in the form Ax+By=C is

Answer 1

Answer:

$\boxed{3x - y = 5}}$

Step-by-step explanation:

The coordinates of the two points are (4, 7) and (3, 4).

(a) Calculate the slope of the line

$\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\&= & \dfrac{7 - 4}{4 - 3}\\\\& = & \dfrac{3}{1}\\\\ & = &3\\\end{array}$

(b) Calculate the y-intercept

$\begin{array}{rcl}y & = & mx + b\\7 & = & 3 \times 4 + b\\7 & = & 12 + b\\b & = & -5\\\end{array}$

(c) Write the equation for the line

y = 3x - 5

This is the point-slope form of the equation.

(d) Convert to standard form

$\begin{array}{rcl}y & = & 3x - 5\\-3x + y & = & -5\\3x - y & = & -5\\\end{array}\\\text{The standard form of the equation is }\boxed{\mathbf{3x- y = -5}}$

Answer 2

The equation of the line in the form of Ax + By = C is 3x - y = 7.

Given that,

The equation of the line in the form Ax +By = C,

Which passes through the points (4, 3) and (3,4).

We have to determine,

The equation of the line.

According to the question,

The equation of the line in the form Ax +By = C,

The co-ordinate passes through the points (4, 3) and (3,4).

To determine the equation of the line following all the steps given below.

• Step1; The slope of the two points can be written as,

                   $m = \dfrac{y_2-y_1}{x_2-x_2}\\\\m = \dfrac{4-7}{3-4}\\\\m = \dfrac{-3}{-1}\\\\m = 3$

                The slope of the line is 3.

• Step2; The y-intercept of the line,

                    $y = mx + c\\\\7= 3 \times 4 + c\\\\7 = 12+ c\\\\c = 7-12\\\\c = -5$

                    The y-intercept of the line is -7.

             

• Step3; The equation for the line is,

                     $y = mx + c \\\\y = 3x-7$

• Step4; The equation can be written as standard form,

                    $y = 3x - 7\\\\3x -y = 7$

Hence, The equation of the line in the form of Ax + By = C is 3x - y = 7.

To know more about Linear equations click the link given below.

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