Question

what is the slope of a line that is parallel to the line shown on the graph? $-\frac{1}{4}$, 4, $-4$, $\frac{1}{4}$ (partial option shown)

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -3)\) and \((4, -2)\).

Step2: Calculate the slope using the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, -3)\) and \((x_2,y_2)=(4, -2)\). Then \(m=\frac{-2 - (-3)}{4 - 0}=\frac{-2 + 3}{4}=\frac{1}{4}\)? Wait, no, wait. Wait, let's check the graph again. Wait, maybe I picked the wrong points. Wait, looking at the graph, the line goes through, for example, \((0, -3)\) and \((4, -2)\)? Wait, no, maybe \((0, -3)\) and \((4, -2)\) – wait, no, let's recalculate. Wait, the y-intercept is at \((0, -3)\), and then when x increases by 4, y increases by 1? Wait, no, maybe I made a mistake. Wait, let's take two clear points. Let's take \((0, -3)\) and \((4, -2)\): the change in y is \(-2 - (-3)=1\), change in x is \(4 - 0 = 4\), so slope is \(\frac{1}{4}\)? But wait, the options have \(\frac{1}{4}\) as the last option (though the last option is cut off, but looking at the options, the first is \(-\frac{1}{4}\), second 4, third -4, fourth maybe \(\frac{1}{4}\)). Wait, but parallel lines have the same slope. Wait, maybe I picked the wrong points. Wait, let's check the graph again. The line is rising from left to right, so slope should be positive. Let's take another pair: \((-4, -4)\) and \((0, -3)\). Then change in y is \(-3 - (-4)=1\), change in x is \(0 - (-4)=4\), so slope is \(\frac{1}{4}\). Wait, but the options: the first option is \(-\frac{1}{4}\), second 4, third -4, fourth (probably \(\frac{1}{4}\)). Wait, maybe I messed up the direction. Wait, no, the line is going from left to right, upwards, so slope is positive. Wait, but let's check again. Wait, the graph: the y-axis is from -7 to 7, x-axis from -7 to 7. The red line: when x=0, y=-3; when x=4, y=-2. So the slope is \(\frac{-2 - (-3)}{4 - 0}=\frac{1}{4}\). But wait, the options – wait, maybe I made a mistake. Wait, no, maybe the points are \((0, -3)\) and \((-4, -4)\): change in y is \(-4 - (-3)=-1\), change in x is \(-4 - 0=-4\), so slope is \(\frac{-1}{-4}=\frac{1}{4}\). So the slope of the given line is \(\frac{1}{4}\), so a parallel line has the same slope, which is \(\frac{1}{4}\). But wait, the options: the first is \(-\frac{1}{4}\), second 4, third -4, fourth (probably \(\frac{1}{4}\)). So the correct answer should be \(\frac{1}{4}\), but since the last option is cut off, but based on the calculation, the slope is \(\frac{1}{4}\), so the parallel line has the same slope, \(\frac{1}{4}\). Wait, but maybe I made a mistake. Wait, let's check again. Let's take two points: (0, -3) and (4, -2). The slope is \(\frac{-2 - (-3)}{4 - 0}=\frac{1}{4}\). Yes, so the slope of the given line is \(\frac{1}{4}\), so a parallel line has the same slope, \(\frac{1}{4}\).

Wait, but the options: the first option is \(-\frac{1}{4}\), second 4, third -4, fourth (let's assume it's \(\frac{1}{4}\)). So the answer is \(\frac{1}{4}\), which is the last option (even though it's cut off, but based on the calculation, the slope is \(\frac{1}{4}\), so parallel lines have the same slope, so the slope of the parallel line is \(\frac{1}{4}\).

Wait, but maybe I messed up the points. Let's check the graph again. The line passes through (0, -3) and (4, -2): yes, that's correct. So slope is \(\frac{1}{4}\), so the parallel line has slope \(\frac{1}{4}\).

Answer:

\(\frac{1}{4}\) (assuming the last option is \(\frac{1}{4}\))