Question

Write the equation of a line in slope intercept form that passes through the points (0, 7) and (5, 3)

Write the equation of a line in point-slope form that has a slope of 1/3 and passes through the point
(-6, 0).

Answer 1

1) Option B
`y=-(4)/(5)x +7`

2) Option A
`y-0=(1)/(3) (x+6)`

Explanation:

Question 1:

We will find the slope of the line with the help of the given points (0, 7) and (5, 3)

.

`Slope_1 = (y_2-y_1)/(x_2-x_1)`

`Slope_1 = (3-7)/(5-0) =-(4)/(5)`

Now, we will use any one of the given points and substitute its x and y coordinates in the standard form of equation of a line to find the y-intercept:

`y=mx+c`

`7=-(4)/(5)(0)+c`

`7=c`

Therefore, the equation of the line 1 is
`y=-(4)/(5) x+7`

Question 2:

We are given the slope of this line and a point (-6, 0) which the line passes through.

`Slope_2=(1)/(3)`

`y-y_1=m(x-x_1)`

`y-0=(1)/(3)(x-(-6))`

`y-0=(1)/(3) (x+6)`

Therefore, the equation of line 2 is
`y-0=(1)/(3) (x+6)`.