Question

2. What is the equation in slope-intercept form of the line that passes through thepoints (-4, 47) and (2, -16)?O21 979y=-2*+ 21Oy=--Źx+97921Oy=-4x+5y=-21*+5--CLEAR ALL

Answer 1

hello

the points given are (-4, 47) and (2, -16)

let's find the intercept of this equation

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ x_2=2 \\ y_2=-16 \\ y_1=47 \\ x_1=-4 \end{gathered}`
`\begin{gathered} m=(-16-47)/(2-(-4)) \\ m=-(21)/(2) \\ slope=-(21)/(2) \end{gathered}`

now, since we know the value of the slope, we can use that in the standard equation on a straight line

the standard equation of a straight line is given as

`\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}`

we can pick any of the points and solve for intercept

let's use (2, -16)

`\begin{gathered} x=2 \\ y=-16 \\ y=mx+c \\ m=-(21)/(2) \\ -16=-(21)/(2)(2)+c \\ -16=-21+c \\ \text{collect like terms} \\ c=-16+21 \\ c=5 \end{gathered}`

now we know the value of intercept (c) = 5 and the slope (m) = 21/2

let's use this to write equation of the straight line

`\begin{gathered} y=mx+c \\ y=-(21)/(2)x+5 \end{gathered}`

from the calculations above, the equation of the straight line is given as y = -21/2x + 5