Answer:
Let's start by finding the x- and y-intercepts. On this graph, the x-intercept (the point where the line intersects the x-axis) is (6, 0). The y-intercept (the point where the line crosses the y-axis) is (0, 4).
With those two points, we can determine the slope. Slope, in simple terms, is the change in y value divided by the change in x value between any two points on the line. Stated mathematically, if you have a point with coordinates (x₁, y₁) and another point with coordinates (x₂, y₂) on the same line, then the slope of the line can be calculated as:
slope = (y₁ - y₂)/(x₁ - x₂)
We already have points (6, 0) and (0, 4), so let's use those.
x₁ = 6
y₁ = 0
x₂ = 0
y₂ = 4
slope = (0 - 4)/(6 - 0) = -4/6 = -2/3
Slope-intercept form is always written as y = mx + b where m is the slope of the line and b is the y-value of the y-intercept. We know that the slope (m) is -2/3 and the y-value of the y-intercept (b) is 4, so the line can be written in slope-intercept form as:
y = (-2/3)x + 4
