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How do you find the slope and intercept of $ y = 4x - 2 $ ?

seo-qna
Last updated date: 13th Jul 2024
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Answer
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Hint: In this question we need to find the slope and intercept of a line whose equation is given to us. To find the slope and intercept of a line from its equation, we first need to convert the given equation of line into slope-intercept form of straight line. The standard form of equation of line is $ y = mx + c $ .

Complete step-by-step solution:
 Let us try to find the slope and intercept of a line whose equation is given to us. To find slope and intercept of line we need to convert our given equation into slope-intercept form of straight line. The equation of straight line in slope-intercept form is given by $ y = mx + c $ , where $ m $ is the slope of line and $ c $ is the intercept of line. The slope of a line defines direction and its steepness. The intercept is the point where the line cuts the y-axis.
Equation of the line whose slope and intercept we need to find is $ y = 4x - 2 $ .
We will first convert the given equation of straight line into slope-intercept form of straight line. Since, the given equation of straight line is already in slope intercept form.
Now, we know that in slope-intercept form of straight line $ y = mx + c $ , $ m $ is slope and $ c $ is the intercept of line.
On comparing the given equation of line $ y = 4x - 2 $ and its general equation, we get
 $ m = 4 $ And
 $ c = - 2 $
Hence the slope is equal to $ 4 $ and the intercept is equal to $ - 2 $ for line with equation $ y = 4x - 2 $ .

Note: Two straight lines are parallel if they same slope and different intercept for, example: $ y = mx + {c_1} $ and $ y = mx + {c_2} $ where $ {c_1} \ne {c_2} $ are parallel. A straight line is perpendicular to $ x $ axis and parallel to $ y $ axis if its equation is of the form $ x = c $ . A straight line is parallel to $ x $ axis and perpendicular to $ y $ axis if its equation of the form $ y = c $ .