Question

A graphed line has a slope of 4 and passes through the point (-1,1)

Answer 1

To write the equation of a line with a given slope and a point it passes through, you can use the point-slope form of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.

In your case:
- The slope \( m = 4 \)
- The point is \( (x_1, y_1) = (-1, 1) \)

Plugging these values into the point-slope form:

\[
y - 1 = 4(x - (-1))
\]

This simplifies to:

\[
y - 1 = 4(x + 1)
\]

Expanding the equation:

\[
y - 1 = 4x + 4
\]

Now, adding 1 to both sides:

\[
y = 4x + 4 + 1
\]

So, the final equation of the line is:

\[
y = 4x + 5
\]

This is the equation of the line with a slope of 4 that passes through the point (-1, 1).