Question

Graph ​ y−2=−34(x−6) ​ using the point and slope given in the equation.

Use the line tool and select two points on the line.

Answer 1

the points are at (8,0) and (0,6)

Answer 2

Point-slope form: An equation of a straight line in the form
`y -y_1 = m(x -x_1)`;

where

m is the slope of the line and
`(x_1, y_1)` are the coordinates of a given point on the line.

Given the equation:
`y-2=-(3)/(4)(x-6)` ......[1]

On comparing with Point slope form equation we have;

m =
`-(3)/(4)` and point (6 , 2)

Now, find the Intercept of the given equation:

x-intercept: The graph crosses the the x-axis i.e,

Substitute y =0 in [1] and solve for x;

`0-2=-(3)/(4)(x-6)`

`-2=-(3)/(4)(x-6)`

Using distributive property:
`a\cdot(b+c) = a\cdot b +a\cdot c`

`-2 = -(3)/(4)x + (18)/(4)`

Subtract
`(18)/(4)` on both sides we get;

`-2-(18)/(4)= -(3)/(4)x + (18)/(4) -(18)/(4)`

Simplify:

`-(26)/(4) = -(3)/(4)x`

or

-26 = -3x

Divide both sides by -3 we get;

x = 8.667

x-intercept: (8.667, 0)

Similarly, for

y-intercept:

Substitute x = 0 in [1] and solve for y;

`y-2=-(3)/(4)(0-6)`

`y-2=(18)/(4)`

Add 2 on both sides we get;

`y-2+2=(18)/(4)+2`

Simplify:

`y=(26)/(4) =6.5`

y-intercept: (0, 6.5)

Now, using these two points (8.667, 0) and (0, 6.5) you can plot the graph using line tool as shown below.