Question

Use the point highlighted in the graph below to write the equation in point slope form for the line provided.

Answer 1

Making the equation of the graph using the Point-Slope Form:

`\text{ y - y}_1=m(x-x_1)`

Since slope was not given, let's compute first for the slope (m) using this formula,

`\text{ m = }\frac{y_2-y_1}{x_2-x_1_{}}`

From the graph, we have one set of coordinates given: (2, 3)

However, we cannot solve the slope with one point alone, thus let's find another point that's along the line and easier to find. From the graph, we get (0,4).

Let's now compute for the slope (m).

`(x_1,y_1)=(0,4);(x_(2,)y_2)=(2,3)_{}`
`\text{ m = }\frac{3\text{ - 4}}{2\text{ - 0}}\text{ = }(-1)/(2)`

Let's now make the equation using the Point-Slope Form using (2,3) as (x1,y2),

`\text{ y - y}_1=m(x-x_1)`
`\text{ y - 3 = (}(-1)/(2))(x-\text{ 2)}`
`\text{ y - 3 + 3 = -}(1)/(2)x\text{ + }(2)/(2)\text{ + 3}`
`\text{ y = }(-1)/(2)x\text{ + 1 + 3 = }(-1)/(2)x\text{ + 4}`

Thus, the equation of the line is,

`\text{ y = }(-1)/(2)x\text{ + 4}`