Use point-slope form to write the equation of a line that passes through the point left bracket, 8, comma, 17, right bracket
(
8
,
17
)
(8,17) with slope start fraction, 3, divided by, 2, end fraction
3
2
2
3
The equation can be written in point-slope form as:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
y - 17 = (3/2)(x - 8)
To write the equation of a line using the point-slope form, we need the coordinates of a point on the line and the slope of the line.
Given:
Point: (8, 17)
Slope: 3/2
The point-slope form of a linear equation is (y - y1) = m(x - x1), where (x1, y1) denotes the coordinates of a point on the line, and m denotes the slope of the line.
Substituting the given values into the point-slope form:
(y - 17) = (3/2)(x - 8)
Distribute the 3/2 to x and -8:
y - 17 = (3/2)x - 3(3/2)
Simplify:
y - 17 = (3/2)x - 9/2
Move -17 to the right side:
y = (3/2)x - 9/2 + 17
Combine like terms:
y = (3/2)x - 9/2 + 34/2
y = (3/2)x + 25/2
Therefore, the equation of the line passing through the point (8, 17) with a slope of 3/2 in point-slope form is y = (3/2)x + 25/2.
To write the equation of a line using the point-slope form, we need two pieces of information: the slope of the line and a point that the line passes through.
Given the point (8, 17) and the slope 3/2, we can use the point-slope form:
y - y1 = m(x - x1)
Where (x1, y1) represents the given point and m represents the slope.
Substituting the values, we have:
y - 17 = (3/2)(x - 8)
Now, we can simplify this equation to convert it into slope-intercept form, y = mx + b, where b is the y-intercept.
Distributing 3/2 to (x - 8), we get:
y - 17 = (3/2)x - 12
Simplifying further:
y = (3/2)x - 12 + 17
y = (3/2)x + 5
So, the equation of the line in slope-intercept form is y = (3/2)x + 5.