Question

has a slope of and a y-intercept (b) of
options: 1, -1, 0, \\(\frac{4}{5}\\), \\(\frac{5}{4}\\), \\(\frac{4}{3}\\), \\(-\frac{5}{4}\\)

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 1)\) (the y - intercept) and \((- 4,-4)\) (we can find this point by looking at the grid). Wait, actually, let's re - examine. The line passes through \((0,1)\) and another point. Wait, maybe a better way: the y - intercept is where \(x = 0\), so when \(x = 0\), \(y=1\)? Wait, no, looking at the graph, the line passes through \((0,1)\) and \((- 4,-4)\)? Wait, no, let's take two clear points. Let's see, when \(x = 0\), \(y = 1\) (the y - intercept point), and when \(x=-4\), \(y=-4\)? Wait, no, maybe I made a mistake. Wait, the line passes through \((0,1)\) and \((4,5)\)? Wait, let's calculate the slope. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: \((0,1)\) and \((4,5)\). Then \(m=\frac{5 - 1}{4 - 0}=\frac{4}{4} = 1\)? Wait, no, \(\frac{5 - 1}{4-0}=\frac{4}{4}=1\)? Wait, but let's check another pair. If we take \((0,1)\) and \((- 4,-3)\)? No, maybe the correct points are \((0,1)\) and \((4,5)\), so slope \(m = 1\)? Wait, no, wait the y - intercept: when \(x = 0\), the line crosses the y - axis at \((0,1)\)? Wait, the graph shows that the line passes through the origin? No, wait the blue dot is at \((0,1)\)? Wait, the grid: the x - axis and y - axis are from - 5 to 5. The line passes through \((0,1)\) and \((4,5)\), so slope \(m=\frac{5 - 1}{4-0}=\frac{4}{4}=1\)? Wait, no, \(\frac{5 - 1}{4-0}=1\). And the y - intercept is when \(x = 0\), so \(y = 1\). Wait, but let's check again. Wait, maybe the two points are \((0,1)\) and \((- 4,-3)\), no, that would be slope \(\frac{-3 - 1}{-4-0}=\frac{-4}{-4}=1\). So the slope is \(1\), and the y - intercept (when \(x = 0\)) is \(1\). Wait, but let's confirm. The slope formula: \(m=\frac{rise}{run}\). From \((0,1)\) to \((4,5)\), the rise is \(5 - 1 = 4\), the run is \(4 - 0 = 4\), so \(\frac{4}{4}=1\). So the slope \(m = 1\), and the y - intercept \(b = 1\). Wait, but let's check the options. The options for slope: 1, - 1, 0, \(\frac{4}{5}\), \(\frac{5}{4}\), \(\frac{4}{3}\), \(-\frac{5}{4}\). And for y - intercept: let's see, when \(x = 0\), the y - value is 1. So slope is 1, y - intercept is 1.

Wait, maybe I made a mistake. Let's re - examine the graph. The line passes through \((0,1)\) and \((4,5)\), so slope \(m=\frac{5 - 1}{4 - 0}=1\), and y - intercept \(b = 1\).

Step2: Determine the slope and y - intercept

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the line: \((x_1,y_1)=(0,1)\) (y - intercept point) and \((x_2,y_2)=(4,5)\). Then \(m=\frac{5 - 1}{4 - 0}=\frac{4}{4}=1\). The y - intercept \(b\) is the value of \(y\) when \(x = 0\), so from the point \((0,1)\), \(b = 1\).

Answer:

Slope: \(1\), y - intercept: \(1\)