Petra needs to find the equation of a line through (–2, 3) that is parallel to the line represented by y = 2x– 4. Which equation best represents Petra's equation?
The answer is y=2x+7. First put it in point slope form then solve it into slope-intercept form. Use the same slope because having parallel lines means the same slope.
To find the equation of a line that is parallel to a given line, we need to know that parallel lines have the same slope. The given line is in slope-intercept form, y = mx + b, where m is the slope of the line.
In the given line, y = 2x - 4, the slope is 2. Therefore, any line that is parallel to this line will also have a slope of 2.
Now, we know that a line with a slope of 2 passing through the point (-2, 3) can be represented using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values (-2, 3) and m = 2 into the equation, we get:
y - 3 = 2(x - (-2))
Simplifying the equation:
y - 3 = 2(x + 2)
y - 3 = 2x + 4
Now, rearranging the equation to the slope-intercept form:
y = 2x + 4 + 3
y = 2x + 7
Therefore, the equation that best represents Petra's equation is y = 2x + 7.