Question

consider the motion indicated by the graph below. write the equation of the line (in slope-intercept form) represented below.

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at (0, 4)? Wait, no, looking at the graph, the y-intercept (where x=0) is at (0, 4)? Wait, no, the grid: let's check. Wait, the graph shows the line passes through (0, 4)? Wait, no, maybe (0, 4) or (0, 3)? Wait, no, let's re-examine. Wait, the y-axis: when x=0, the line is at y=4? Wait, no, maybe I misread. Wait, the graph: the line crosses the y-axis at (0, 4)? Wait, no, let's check the points. Wait, another point: when x=2, y=0? Wait, no, the x-intercept is at (2, 0)? Wait, no, the grid: each square is 1 unit. So from (0, 4) to (2, 0): the slope would be (0 - 4)/(2 - 0) = -4/2 = -2? Wait, no, maybe the y-intercept is (0, 4) and x-intercept (2, 0). Wait, no, let's look again. Wait, the graph: the line goes through (0, 4) and (2, 0)? Wait, no, maybe (0, 4) and (2, 0). Wait, slope-intercept form is y = mx + b, where b is y-intercept. Let's find two points. From the graph, when x=0, y=4? Wait, no, the original graph: wait, the user's graph: the y-axis has 5, 10, etc. Wait, maybe the y-intercept is (0, 4)? No, wait, the grid: let's see, the line crosses the y-axis at (0, 4)? Wait, no, maybe (0, 4) is wrong. Wait, let's check the x-intercept: when y=0, x=2? So two points: (0, 4) and (2, 0). Then slope m = (0 - 4)/(2 - 0) = -4/2 = -2. Then y-intercept b is 4. So equation is y = -2x + 4? Wait, no, maybe I made a mistake. Wait, let's check again. Wait, the graph: the line passes through (0, 4) and (2, 0). So slope is (0 - 4)/(2 - 0) = -2. So equation is y = -2x + 4. Wait, but maybe the y-intercept is (0, 4) and slope -2. So that's the equation.

Wait, no, maybe the y-intercept is (0, 4) and the line goes down 2, right 1? Wait, no, from (0, 4) to (1, 2), then (2, 0). So slope is (2 - 4)/(1 - 0) = -2. So yes, slope is -2, y-intercept 4. So equation is y = -2x + 4.

Wait, but let's confirm. Slope-intercept form is y = mx + b, where m is slope, b is y-intercept.

Step1: Find y-intercept (b)

The line crosses the y-axis at (0, 4), so b = 4.

Step2: Calculate slope (m)

Take two points: (0, 4) and (2, 0). Slope m = (y2 - y1)/(x2 - x1) = (0 - 4)/(2 - 0) = -4/2 = -2.

Step3: Write equation

Using y = mx + b, substitute m = -2 and b = 4: y = -2x + 4.

Wait, but maybe the y-intercept is (0, 4) and x-intercept (2, 0). So that's correct.

Answer:

$y = -2x + 4$