What is the equation of a line in slope intercept form, given that the slope of the line is 1 and a point on the line is $(-2,0)$?
A. $y=x-2$
B. $y=2 x+1$
C. $y=x+2$
D. $y=2 x-1
Answer (2)
Substitute the given slope m = 1 and point ( − 2 , 0 ) into the point-slope form: y − 0 = 1 ( x − ( − 2 )) .
Simplify the equation: y = x + 2 .
The equation of the line in slope-intercept form is y = x + 2 .
The final answer is y = x + 2 .
Explanation
Understanding the Problem We are given the slope of a line, which is m = 1 , and a point on the line, which is ( − 2 , 0 ) . We want to find the equation of the line in slope-intercept form, which is y = m x + b , where m is the slope and b is the y-intercept.
Using Point-Slope Form We can use the point-slope form of a line, which is y − y 1 = m ( x − x 1 ) , where m is the slope and ( x 1 , y 1 ) is a point on the line.
Substituting Values Substitute the given slope m = 1 and the point ( − 2 , 0 ) into the point-slope form:
y − 0 = 1 ( x − ( − 2 ))
Simplifying the Equation Simplify the equation:
y = 1 ( x + 2 )
y = x + 2
Finding the Equation The equation of the line in slope-intercept form is y = x + 2 .
Examples
Understanding linear equations is crucial in many real-world applications. For instance, if you're tracking the distance you travel over time at a constant speed, the relationship can be modeled with a linear equation. If you start 2 miles from home and walk at a pace of 1 mile per hour, your distance y from home after x hours can be represented as y = x + 2 . This equation allows you to predict your distance from home at any given time, showcasing the practical use of linear equations in everyday scenarios.
The equation of the line in slope-intercept form, given the slope of 1 and the point (-2, 0), is y = x + 2 . Therefore, the correct answer from the options is C. y = x + 2 .
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