Use the image to answer the question.

A line is drawn on a coordinate plane. The x-axis ranges from negative 4 to 4 and the y-axis ranges from negative 6 to 8 in unit increments.

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)
.

1 answer

To complete the point-slope form of the linear equation provided, we need to determine the values for the point given in the form \(y - y_1 = m(x - x_1)\).

In your case, the equation is \(y - \text{missing value} = -3(x - 1)\). Here, \(m\) (the slope) is -3 and \(x_1\) is 1.

To find \(y_1\) (the missing value), we need a point on the line. Since the slope \(m = -3\), we know that for every increase of 1 in \(x\), \(y\) will decrease by 3.

If we assume the point is \( (1, y_1) \), we can find \(y_1\).

  • If the line passes through \(x = 1\), we can evaluate it to find \(y_1\). We might typically have a point such as (1, -3) on the line, assuming it goes downward.

If you have a specific point where the line crosses, substitute it in to complete the equation. If \((1, y_1)\) gives a point part of this line, that’s typically used.

If we take \(y_1 = -3\) as the possible value, the complete equation becomes:

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

Thus, the missing value is \(-3\).