Question

write the equation of this line in slope-intercept form.

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at (0, 1)? Wait, no, looking at the graph, when x=0, y=1? Wait, no, let's check again. Wait, the line passes through (0,1)? Wait, no, maybe I made a mistake. Wait, the grid: each square is 1 unit. Let's see, when x=0, the line is at y=1? Wait, no, wait the line goes through (0,1) and (1, -3)? Wait, no, let's take two points. Let's see, when x=0, y=1? Wait, no, maybe (0,1) and (1, -3)? Wait, no, let's calculate the slope. Wait, slope-intercept form is \( y = mx + b \), where \( b \) is the y-intercept (the value of y when x=0). From the graph, when x=0, the line intersects the y-axis at (0, 1)? Wait, no, looking at the graph, the line passes through (0,1) and (1, -3)? Wait, no, let's check the points. Let's take (0,1) and (1, -3). Then the slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 1}{1 - 0} = -4 \). Wait, but maybe another point. Wait, maybe (0,1) and (2, -7)? Then slope is \( \frac{-7 - 1}{2 - 0} = -4 \). So slope \( m = -4 \), y-intercept \( b = 1 \)? Wait, no, wait the graph: when x=0, the line is at y=1? Wait, maybe I misread. Wait, the line goes through (0,1) and (1, -3), so slope is -4, y-intercept is 1. Wait, but let's check again. Wait, the line in the graph: when x=0, y=1, and when x=1, y= -3. So the slope is \( \frac{-3 - 1}{1 - 0} = -4 \). So the equation is \( y = -4x + 1 \)? Wait, no, wait maybe I made a mistake. Wait, let's check the graph again. Wait, the line passes through (0,1) and (1, -3)? Wait, no, maybe (0,1) and (0.5, -1)? Wait, no, the grid is 1 unit per square. Let's see, from (0,1) to (1, -3): that's a run of 1, rise of -4, so slope -4. So the equation is \( y = -4x + 1 \)? Wait, but let's confirm with another point. If x=2, then y = -4*2 +1 = -7, which is on the graph (2, -7). Yes, that matches. So the y-intercept \( b \) is 1, slope \( m \) is -4.

Step2: Write the equation in slope-intercept form

Slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. We found \( m = -4 \) and \( b = 1 \), so the equation is \( y = -4x + 1 \). Wait, but wait, maybe I made a mistake in the y-intercept. Wait, let's check again. When x=0, the line is at y=1? Yes, because the line crosses the y-axis at (0,1). So \( b = 1 \), slope \( m = -4 \). So the equation is \( y = -4x + 1 \).

Answer:

\( y = -4x + 1 \)