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15 votes
15 votes
Which is an equation of the line that has a slope of 1/2 and passes through the point (3, -1)?

User Ranjit Iyer
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3.3k points

2 Answers

11 votes
11 votes

Answer:

y + 1 = (1/2)(x - 3) - point-slope form

OR

y = (1/2)x - 5/2 - slope-intercept form

Explanation:

Given a slope and point, use point-slope form to write the equation for the line:

y - y1 = m(x - x1)

(x1, y1) is the point given and m is the slope.

y - (-1) = (1/2)(x - 3)

y + 1 = (1/2)(x - 3)

If you need to rewrite in slope intercept form, you can do so by distributing the 1/2 to the x - 3 and subtracting 1 from both sides:

y + 1 = (1/2)x - 3/2

y = (1/2)x - 5/2

User Lovesh
by
3.0k points
16 votes
16 votes

Answer:


\boxed {\boxed {\sf y= \frac {1}{2}x - \frac {5}{2}}}

Explanation:

The equation of a line can be found using the point-slope formula.


y-y_1=m(x-x_1)

where m is the slope and (x₁, y₁) is the point the line passes through. For this line, the slope is 1/2 and the point is (3, -1). Therefore,


m= \frac {1}{2} \\x_1= 3 \\y_1= -1

Substitute the values into the formula.


y--1= \frac {1}{2}(x-3)


y+1= \frac {1}{2}(x-3)

The equation can be left like this, or put into slope-intercept form (y=mx+b).

First, distribute the 1/2. Multiply each term inside the parentheses by 1/2.


y+1= \frac {1}{2}x - \frac {3}{2}

Next, subtract 1 from both sides of the equation.


y+1-1= \frac {1}{2}x - \frac {3}{2}-1


y= \frac {1}{2}x - \frac {5}{2}

User Alex Reynolds
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3.0k points