Question

Given g(x)=x^2-5x, find the equation of the secant line passing through (-3,g(-3)) and (4g(4)). Write your answer in form of y=mx+b

Answer 1

Given:

`g(x)=x^2-5x\text{ ; (}-3,g(-3)),(4,g(4))`
`g(-3)=(-3)^2-5(-3)`
`g(-3)=9+15`
`g(-3)=24`
`g(4)=4^2-5(4)`
`g(4)=16-20`
`g(4)=-4`

Equation of line with the points (-3,24) and (4,-4)

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`
`\frac{y-24_{}}{-4_{}-24_{}}=\frac{x+3_{}}{4_{}+3_{}}`
`\frac{y-24_{}}{-28_{}}=\frac{x+3_{}}{7_{}}`
`\frac{y-24_{}}{-4_{}}=\frac{x+3_{}}{1_{}}`
`y-24_{}_{}=-4(x+3)_{}_{}`
`y_{}=-4x-12+24`
`y=-4x+12`