Questions: Find the slope and the y-intercept of the graph of the linear equation. Then write the equation of the line in slope-intercept form. The slope is □ (Simplify your answer.)

Find the slope and the y-intercept of the graph of the linear equation. Then write the equation of the line in slope-intercept form. The slope is □ (Simplify your answer.)
Transcript text: Find the slope and the $y$-intercept of the graph of the linear equation. Then write the equation of the line in slope-intercept form. The slope is $\square$ (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Identify two points on the line

From the graph, we can identify two points on the line. Let's choose the points (0, 4) and (4, 0).

Step 2: Calculate the slope

The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points (0, 4) and (4, 0): \[ m = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1 \]

Step 3: Determine the y-intercept

The y-intercept is the value of \( y \) when \( x = 0 \). From the graph, we see that the line crosses the y-axis at (0, 4). Therefore, the y-intercept \( b \) is 4.

Step 4: Write the equation in slope-intercept form

The slope-intercept form of a line is given by: \[ y = mx + b \] Substituting the slope \( m = -1 \) and the y-intercept \( b = 4 \): \[ y = -1x + 4 \] or simply, \[ y = -x + 4 \]

Final Answer

The slope is \(-1\) and the equation of the line in slope-intercept form is \( y = -x + 4 \).

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