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How do you write the equation in point slope form given $\left( { - 1,4} \right)$ parallel to $y = - 5x + 2$ ?

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Last updated date: 26th Feb 2024
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IVSAT 2024
Answer
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Hint: To solve these questions, we just have to substitute the correct information given in the question in the formula $y - {y_1} = m(x - {x_1})$ . The point given on the line is substituted in the formula and the slope of the line is found out by the information given in the question.

Formula Used: Point Slope Form of a line is represented by $y - {y_1} = m(x - {x_1})$ where $m$is the slope/gradient of the line and $({x_1},{y_1})$ is a point lying on the line whose equation has to be written.

Complete step by step answer:
Given equation $y = - 5x + 2$ is in the slope-intercept form of a line, that is $y = mx + c$ .
On comparing the two equations we get the slope of the line $m$ as $- 5$ .
Also, we know that when two lines are parallel their slope or gradient are also the same. Therefore, the slope of the line whose equation has to be written is the same as the slope of the line whose equation is given in the question.
Also, the point on the line is given as $\left( { - 1,4} \right)$ , therefore in this case $({x_1},{y_1})$ is $\left( { - 1,4} \right)$
Substituting all the values in the equation of point slope form, we get;
$y - 4 = - 5\left( {x - \left( { - 1} \right)} \right)$
Simplifying the above equation
$\Rightarrow y - 4 = - 5\left( {x + 1} \right)$

Hence, the equation of the line in the point slope form can be given as $y - 4 = - 5\left( {x + 1} \right)$

Note: The equation of a line can be written in mainly three ways which include: the Slope intercept form, Point Slope form, and the General Equation of a line.
The Slope intercept form is written as $y = mx + c$ where $c$ is the intercept cut by the line on the $y$- axis and $m$ is the slope of the line.
The General Equation of a line is given as $ax + by = c$ where $a$ , $b$ and $c$ are constants.
The point slope form has been explained in detail in the solution given above.