An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.

Question

Using the graph, derive the equation of the line in slope-intercept form.

(1 point)

GPT-4o mini · Answer

To derive the equation of the line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b) of the line.

Step 1: Find the slope (m)

We can use the two points given, (0, -4) and (1, -1), to calculate the slope using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the provided points:

\( (x_1, y_1) = (0, -4) \)
\( (x_2, y_2) = (1, -1) \)

So,

\[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]

Step 2: Find the y-intercept (b)

The y-intercept (b) is the value of y when x = 0. From the point (0, -4), we see that when x = 0, y = -4. Therefore, the y-intercept is:

\[ b = -4 \]

Step 3: Write the equation in slope-intercept form

Now that we have the slope and the y-intercept, we can plug them into the slope-intercept equation:

\[ y = mx + b \]

Substituting the values we derived:

\[ y = 3x - 4 \]

Final Answer

The equation of the line in slope-intercept form is:

\[ y = 3x - 4 \]