Write an equation of the line that passes through the given point and has the given slope.
(4, 2); slope 1/2
Write an equation of the line that passes through the given point and has the given slope. (4, 2); slope 1/2
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Write an equation of the line that passes through the given point and has the given slope.
(4, 2); slope 1/2
To write the equation of the line that passes through the point (4, 2) with a slope of 1/2, we can use the point-slope form of the equation of a line, which is:
[
y – y_1 = m(x – x_1)
]
where ( (x_1, y_1) ) is the point on the line and ( m ) is the slope.
1. Plug in the point ( (4, 2) ) for ( (x_1, y_1) ) and the slope ( m = frac{1}{2} ):
[
y – 2 = frac{1}{2}(x – 4)
]
2. To write it in slope-intercept form (y = mx + b), simplify the equation:
[
y – 2 = frac{1}{2}x – 2
]
3. Add 2 to both sides:
[
y = frac{1}{2}x
]
This can also be expressed in standard form if needed, but the slope-intercept form is typically useful.
So the equation of the line is:
[
y = frac{1}{2}x
]
Feel free to ask if you have more questions or need further clarification!