Question

What is the y-intercept of a line that has a slope of 3 and passes through point (–1, –7)?
–10
–4
3
7

Answer 1

To find the y-intercept of a line, you can use the point-slope form of a linear equation:

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

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

In this case, the slope \(m = 3\) and the point is \((-1, -7)\). Substituting these values into the equation gives:

\[
y - (-7) = 3(x - (-1))
\]

This simplifies to:

\[
y + 7 = 3(x + 1)
\]

Now simplify the right side:

\[
y + 7 = 3x + 3
\]

Next, isolate \(y\):

\[
y = 3x + 3 - 7
\]

\[
y = 3x - 4
\]

From the equation \(y = 3x - 4\), we can see that the y-intercept (the value of \(y\) when \(x = 0\)) is \(-4\).

Thus, the y-intercept of the line is:

\(-4\)