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 2. Image with alt text: y equals 2 x plus 4. Image with alt text: y equals 4 x.
Since the line we are trying to find is parallel to the given line, it will have the same slope. The given line has a slope of 2, so the slope of the new line will also be 2.
We are also given a point that the new line passes through, but no specific point is mentioned in the description. Therefore, any point that lies on the given line can be used. Let's choose the point (0,4), which lies on the given line y = 2x + 4.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values to find the equation of the new line:
y - 4 = 2(x - 0)
Expanding the equation:
y - 4 = 2x
To write it in slope-intercept form (y = mx + b), we isolate y:
y = 2x + 4
Therefore, the equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation y = 2x + 4 is y = 2x + 4.