Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. ; (1 point) Responses Image with alt text: y equals negative 2 x. Image with alt text: y equals 2 x. Image with alt text: y equals one-half x.
To write the equation of a line parallel to y = -2x, we need to know a point that the line passes through. Without this information, we cannot determine a unique equation.
To find the equation of a line that passes through a given point and is parallel to a given line, we need to use the slope-intercept form of the equation.
The given equation is: y = -2x
Since we are looking for a line parallel to this, the slope of the new line will also be -2.
Let's say the given point is (a, b).
Using the point-slope form of a linear equation, we can write the equation of the new line as:
y - b = -2(x - a)
To convert this equation into slope-intercept form (y = mx + b), we need to simplify it.
Expanding the equation gives us:
y - b = -2x + 2a
Rearranging the terms, we have:
y = -2x + 2a + b
Therefore, the equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of y = -2x is:
y = -2x + (2a + b)
To find the equation of a line in slope-intercept form that passes through a given point and is parallel to a given line, you need to use the following steps:
1. Identify the slope of the given line.
- In this case, the given line is y = -2x, which means the slope is -2.
2. Parallel lines have the same slope, so the line you need to find will also have a slope of -2.
3. Use the point-slope form of a line to write the equation.
- The point-slope form of a line is: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
- Let's say the given point is (x1, y1) = (a, b), where a is the x-coordinate and b is the y-coordinate.
4. Substitute the given point (a, b) and the slope (-2) into the point-slope form.
- The equation will then be: y - b = -2(x - a)
5. Simplify the equation to the slope-intercept form.
- Distribute the -2 to the terms inside the parentheses: y - b = -2x + 2a
6. Rearrange the equation to isolate y.
- Add b to both sides of the equation: y = -2x + 2a + b
Therefore, the equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of y = -2x is y = -2x + 2a + b.