Question

What is the equation of the line that passes through the (-6, 1) slope -3/2?

Answer 1

Given the question:

Point (x,y) = -6,1

Slope (m) = -3/2

Let's use the Slope-Intercept Formula in making the equation of the line.

`\text{ y = mx + b}`

Step 1: Substituting m = -3/2 and x,y = -6,1 in y = mx + b, let's determine the value of the y-intercept (b).

`\text{ y = mx + b }\rightarrow\text{ 1 = (-}(3)/(2))(-6)\text{ + b}`
`\text{ 1 = }(18)/(2)\text{ + b }\rightarrow\text{ 1 = 9 + b}`
`1\text{ - 9 = 9 + b - 9}`
`-8\text{ = b ; b = -8}`

Step 2: Let's now complete the equation by substituting m = -3/2 and b = -8 in the formula.

`\text{ y = mx + b}`
`\text{ y = (-}(3)/(2))x\text{ + (-8)}`
`\text{ y = -}(3)/(2)x\text{ - }8`

Therefore, the equation of the line is y = (-3/2)x - 8.