Find the line that passes through the point (0, 2) and is parallel to the line y = -7/3x - 4.
a.)y = -7/3x + 2
b.)y = 7/3x - 4
c.)y = 3/7x - 4
m = -7/3
y = -7x/3 + b
2 = 0 + b
b = 2
so
y = -7x/3 + 2
a
Thanks:)
To find a line that is parallel to a given line and passes through a given point, follow these steps:
1. Determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope of the line.
In this case, the given line is y = -7/3x - 4. Comparing it to the slope-intercept form, we can see that the slope (m) of the given line is -7/3.
2. Since a line parallel to another line will have the same slope, the line we are looking for will also have a slope of -7/3.
3. Use the point-slope form of a line to find the equation of the line. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
In this case, the point we need to pass through is (0, 2) and the slope is -7/3. Substituting these values into the point-slope form, we get:
y - 2 = -7/3(x - 0)
Simplifying the equation further:
y - 2 = -7/3x
4. Finally, rewrite the equation in slope-intercept form (y = mx + b), where b is the y-intercept.
y - 2 = -7/3x
To isolate y, we add 2 to both sides:
y = -7/3x + 2
Therefore, the line that passes through the point (0, 2) and is parallel to the line y = -7/3x - 4 is represented by the equation:
a.) y = -7/3x + 2.