Question

Write the equation in slope-intercept form for the line that goes through (-8, -2) and (-4, 6)

Answer 1

The equation of a line in slope-intercept form is given as:

`\begin{gathered} y=mx+c \\ ^(\prime)m^(\prime)\text{ is the slope} \\ ^(\prime)c^(\prime)\text{ is the intercept on y-axis} \end{gathered}`

The slope,m, is calculated using the formula:

`m=(y_2-y_1)/(x_2-x_1)`
`\begin{gathered} \text{For the points (-8,}-2)\text{ and (-4,6)} \\ x_1=-8,y_1=-2_{}_{}_{} \\ x_2=-4,y_2=6 \end{gathered}`

Thus,

`\begin{gathered} m=(6-(-2))/(-4-(-8)) \\ m=(6+2)/(-4+8) \\ m=(8)/(4) \\ m=2 \end{gathered}`
`\begin{gathered} Equation\text{ of the line is:} \\ m=(y-y_1)/(x-x_1) \\ 2=(y-(-2))/(x-(-8)) \\ 2=(y+2)/(x+8) \\ y+2=2(x+8) \\ y+2=2x+16 \\ y=2x+16-2 \\ y=2x+14 \end{gathered}`

Hence, the equation of the line in slope-intercept form is:

y= 2x + 14