Question

Identify the equation of the graphwrite the equation in slope intercept form

Answer 1

To be able to determine the equation of the graph, we must first identify at least two points that pass through the graph and use it to generate the equation.

From the given graph, we identified two points:

Point A : x1,y1 = -2, 0

Point B : x2,y2 = 0, -3

Step 1: Let's determine the slope of the line (m).

`\text{ m = }(y_2-y_1)/(x_2-x_1)`
`\text{ = }\frac{-3\text{ - 0}}{0\text{ - (-2)}}\text{ = }\frac{-3\text{ - 0}}{0\text{ + 2}}`
`\text{ m = -}(3)/(2)`

Step 2: Let's determine the y-intercept (b). Substitute m = -3/2 and x,y = 0, -3 in y = mx + b.

`\text{ y = mx + b}`
`\text{ -3 = (-}(3)/(2))(0)\text{ + b}`
`\text{ -3 = 0 + b}`
`\text{ -3 = b}`

Step 3: Let's complete the equation. Substitute the m = -3/2 and b = -3 in y = mx + b.

`\text{ y = mx + b}`
`\text{ y = (-}(3)/(2))x\text{ + (-3)}`
`\text{ y = -}(3)/(2)x\text{ - 3}`

Therefore, the equation of the graph is y = -3/2x - 3.