Question

identify the slope and y-intercept of the line below.
draw
slope =
y-intercept =

Explanation:

Step1: Find two points on the line

From the graph, we can identify two points: \((0, -6)\) (the y - intercept point) and \((3, -1)\) (wait, no, let's check again. Wait, another point: let's take \((0, -6)\) and \((2, -2)\)? Wait, no, looking at the blue dots: one is at \((0, -6)\) (since it's on the y - axis, x = 0) and another at \((3, -1)\)? Wait, no, let's calculate the slope using two clear points. Let's take \((-2, -11)\) and \((0, -6)\)? Wait, maybe better to use \((0, -6)\) and \((3, 3)\)? Wait, no, let's look at the grid. The y - intercept is where x = 0, so when x = 0, y=-6, so the point is \((0, -6)\). Another point: let's take when x = 3, y = 3? Wait, no, the line passes through \((3, -1)\)? Wait, no, let's count the rise over run. From \((0, -6)\) to \((3, 3)\)? Wait, no, maybe I made a mistake. Let's take two points: \((0, -6)\) and \((2, -2)\)? Wait, no, let's use the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take the point \((0, -6)\) (x₁ = 0, y₁=-6) and \((3, 3)\)? Wait, no, looking at the graph, when x = 3, the y - value: let's see the grid. Each square is 1 unit. From (0, -6), moving 3 units to the right (x increases by 3) and how much up? From y=-6 to y = 3? No, that's 9 units up. Wait, no, maybe the points are \((0, -6)\) and \((2, -2)\)? Wait, no, let's check the blue dots. One dot is at \((0, -6)\) (x = 0, y=-6) and another at \((3, -1)\)? Wait, no, let's calculate the slope correctly. Let's take two points: \((0, -6)\) and \((3, 3)\)? Wait, no, let's use \((0, -6)\) and \((2, -2)\). Wait, the difference in y: \(-2-(-6)=4\), difference in x: \(2 - 0 = 2\), so slope \(m=\frac{4}{2}=2\)? Wait, no, that's not right. Wait, maybe the points are \((-2, -10)\) and \((0, -6)\). Then \(y_2 - y_1=-6-(-10)=4\), \(x_2 - x_1=0 - (-2)=2\), so slope \(m = \frac{4}{2}=2\). Wait, no, let's check with \((0, -6)\) and \((3, 3)\): \(y_2 - y_1=3-(-6)=9\), \(x_2 - x_1=3 - 0 = 3\), so \(m=\frac{9}{3}=3\). Ah, that makes sense. So from (0, -6) to (3, 3), x increases by 3, y increases by 9, so slope \(m = 3\). Wait, but let's check another pair. From ( - 2, - 12) to (0, -6): \(y_2 - y_1=-6-(-12)=6\), \(x_2 - x_1=0 - (-2)=2\), so \(m=\frac{6}{2}=3\). Yes, so the slope is 3.

Step2: Find the y - intercept

The y - intercept is the point where the line crosses the y - axis, which is when x = 0. From the graph, when x = 0, y=-6, so the y - intercept is - 6.

Answer:

slope = \(3\)
y - intercept = \(-6\)