Question

What is the slope-intercept form of the equation of the line parallel to the line in the graph that passes through the point (-1, 1)? Item 1 Item 2 (-1,1) -3 -1 -1 1 3 x (2 points) y=2x+5 Oy2x+3 Oy=2x-3 y=2x+3

Answer 1

To find the slope-intercept form of the equation of the line that is parallel to a given line and passes through the point (-1, 1), we first need to determine the slope of the given line. Since you didn't provide the equation of the original line, I'll assume a typical case where a line has a slope of 2 (as inferred from the multiple-choice options you provided).

1. **Parallel Lines**: Lines that are parallel have the same slope. If we assume the slope of the original line is 2, the slope of any line parallel to it will also be 2.

2. **Using the Point-Slope Form**: We can use the point-slope form of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope, and \((x_1, y_1)\) is the point the line passes through.

In our case, the slope \(m = 2\) and the point is \((-1, 1)\):
\[
y - 1 = 2(x - (-1))
\]
\[
y - 1 = 2(x + 1)
\]
\[
y - 1 = 2x + 2
\]
\[
y = 2x + 3
\]

3. **Slope-Intercept Form**: The equation in slope-intercept form is \(y = 2x + 3\).

From the options you provided, the equation that corresponds to our finding is:
\[
y = 2x + 3
\]

So the answer is the equation of the line parallel to the original line that passes through the point (-1, 1) is **y = 2x + 3**.