Question

Given the graph of a linear function, find the linear equation of the graph in point-slope form. What is the missing value needed to finish the point-slope form of the equation?

(1 point)
The point-slope form of the equation is y−
=−3(x−1)
.

Answer 1

The point-slope form of a linear equation is given by the formula:

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

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

From the context, you have the equation:

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

Here, the slope \( m \) is -3, and the \( x \)-coordinate of the point \( (x_1, y_1) \) is 1.

To complete the equation, you need the \( y \)-coordinate \( y_1 \) of the point. The equation says \( y - \_ \), which means you need to find the appropriate value for \( y_1 \).

If you know the point on the graph corresponding to \( x = 1 \), you can find \( y_1 \). Let's say, for example, the value of the function at \( x = 1 \) is 2; then \( y_1 \) would be 2, and the equation would read:

\[
y - 2 = -3(x - 1)
\]

Since you did not provide a specific point, I cannot give you the exact value to finish the equation. But in general, you need the \( y \)-coordinate of the point corresponding to \( x = 1 \).

If the value of \( y_1 \) (the \( y \)-coordinate at \( x_1 = 1 \)) weren't specified, just replace the underscore with the appropriate value.

So, if you had (for example) the point \( (1, 2) \):

The missing value for the equation would be \( 2 \):

Thus, the completed equation would be:

\[
y - 2 = -3(x - 1)
\]