A line passes through (–3, –1) and is parallel to the graph of y = 2x + 3. What equation represents the line in slope-intercept form?
The line is parallel to the graph of y = 2x + 3, which means it has the same slope as that of the given line. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope of the line is 2. We know that the line passes through the point (-3, -1), so we can use the point-slope form of a linear equation to find the y-intercept.
The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Using (-3, -1) as our point and 2 as our slope, we can write the equation in point-slope form:
y - (-1) = 2(x - (-3))
Simplifying the equation:
y + 1 = 2(x + 3)
y + 1 = 2x + 6
Now we can rewrite the equation in slope-intercept form by isolating y:
y = 2x + 6 - 1
y = 2x + 5
Therefore, the equation that represents the line in slope-intercept form is y = 2x + 5.