Question

1. jen graphed a linear equation shown below. which of the follow is a true statement? 1 point a. the graph has a negative y - intercept. b. the graph has a slope of - 2. c. the graph represents $y = - 0.5x + 10$. d. all the above are true.

Explanation:

Step1: Analyze y - intercept

The y - intercept is the value of y when x = 0. From the graph, when x = 0, y = 10, which is positive. So option a is false.

Step2: Calculate the slope

We can use two points on the line. Let's take (0, 10) and (4, 2). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values, we get $m=\frac{2 - 10}{4 - 0}=\frac{- 8}{4}=-2$. Wait, but let's check option c. The equation of a line is $y=mx + b$, where b is the y - intercept. If the equation is $y=-0.5x + 10$, the slope would be - 0.5. But our calculated slope is - 2. Wait, maybe I made a mistake. Wait, let's re - check the points. Wait, the line goes from (0,10) to (4,2). The change in y is 2 - 10=-8, change in x is 4 - 0 = 4. So slope $m=\frac{-8}{4}=-2$. But option c has a slope of - 0.5. Wait, maybe I misread the graph. Wait, maybe the point is (4,2)? Wait, no, let's check the graph again. Wait, the y - axis is from 0 to 10, x - axis from 0 to 10. The line starts at (0,10) and goes to (4,2)? Wait, no, maybe the point is (4,2)? Wait, no, let's calculate the slope between (0,10) and (4,2): slope is (2 - 10)/(4 - 0)=-8/4=-2. But option c is $y = - 0.5x+10$, which has slope - 0.5. Wait, maybe I made a mistake in the points. Wait, maybe the second point is (8,6)? No, the arrow is at (4,2). Wait, maybe the graph is different. Wait, let's re - evaluate. Wait, the y - intercept is 10 (positive), so option a is false. The slope: let's take (0,10) and (4,2). Slope is (2 - 10)/(4 - 0)=-2. So the slope is - 2. Wait, but option c's equation is $y=-0.5x + 10$, which has slope - 0.5. So option c is wrong? Wait, no, maybe I misread the graph. Wait, maybe the point is (4,8)? No, the graph shows the line going down from (0,10) to (4,2). Wait, maybe the question has a typo, but according to the options, let's check again. Wait, option b says the graph has a slope of - 2. Let's confirm the slope. If we take two points (0,10) and (4,2), slope is (2 - 10)/(4 - 0)=-2. So slope is - 2. Option a: y - intercept is 10, which is positive, so a is false. Option c: the equation $y=-0.5x + 10$ has slope - 0.5, which is not equal to our calculated slope of - 2, so c is false. Wait, but that can't be. Wait, maybe I made a mistake in the points. Wait, maybe the line goes from (0,10) to (2,9)? No, the graph shows a steeper line. Wait, maybe the correct answer is b? Wait, let's re - check. The y - intercept is at (0,10), which is positive, so option a is false. The slope between (0,10) and (4,2) is - 2, so option b is true. Option c: the equation $y=-0.5x + 10$ would have a slope of - 0.5, which is not equal to - 2, so c is false. So the correct option is b.

Answer:

b. The graph has a slope of -2.