Question

How do you write the standard form of the equation given $\left( {1,2} \right)$ slope 7?

Answer 1

Hint : Point-slope is the general form $y - {y_1} = m\left( {x - {x_1}} \right)$ for linear equations. It emphasizes the slope of the line and a point on the line i.e., not the y-intercept. Hence, to write the standard form of the equation of the given points and the slope, use the point-slope form formula by substituting the given values and then apply in its standard form as $Ax + By = C$ .
Formula used:
$y - {y_1} = m\left( {x - {x_1}} \right)$
${x_1}$ is the x-coordinate of the point.
${y_1}$ is the y-coordinate of the point.
m is the slope of a line.
x, y are the variables.

Complete step-by-step answer :
Given,
Equation of a line passes through the points: $\left( {{x_1},{y_1}} \right) = \left( {1,2} \right)$
Slope: $m = 7$
We know that, the equation in point-slope form formula is given as:
$y - {y_1} = m\left( {x - {x_1}} \right)$ …………………… 1
As we have the values of ${x_1},{y_1},m$ , hence substitute these values in equation 1 as:
$y - {y_1} = m\left( {x - {x_1}} \right)$
$\Rightarrow y - 2 = 7\left( {x - 1} \right)$ ………………. 2
Now, distribute and simplify the terms of equation 2:
$\Rightarrow y - 2 = 7x - 7$
Now add 2 on both the sides of the equation:
$y - 2 + 2 = 7x - 7 + 2$
As, we know that +2 and -2 implies to zero, hence we get:
$\Rightarrow y = 7x - 7 + 2$
Simplify the terms:
$\Rightarrow y = 7x - 5$
Hence, move y over by subtracting it and move 5 over by adding it, hence now you have your Equation in Standard Form as: $Ax + By = C$
$y = 7x - 5$
$\Rightarrow 7x - y = 5$
Therefore, the standard form of the equation is:
$7x - y = 5$
So, the correct answer is “ $7x - y = 5$ ”.

Note : An equation of a line can be expressed in many ways as: Slope Intercept, Standard or Point-Slope. The equation of a straight line of the form $y - {y_1} = m\left( {x - {x_1}} \right)$ is called its point-slope form. The equation of a straight line of the form $y = mx + b$ is called its slope-intercept form. Hence, these are key points to know while solving the equation of a line.