Question

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

Answer 1

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

Answer 2

Answer:

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: $y-2=-\frac{3}{4}(x-6)$         ......[1]

On comparing with Point slope form equation we have;

m = $-\frac{3}{4}$ 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;

$0-2=-\frac{3}{4}(x-6)$

$-2=-\frac{3}{4}(x-6)$

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

$-2 = -\frac{3}{4}x + \frac{18}{4}$

Subtract $\frac{18}{4}$ on both sides we get;

$-2-\frac{18}{4}= -\frac{3}{4}x + \frac{18}{4} -\frac{18}{4}$

Simplify:

$-\frac{26}{4} = -\frac{3}{4}x$

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;

$y-2=-\frac{3}{4}(0-6)$

$y-2=\frac{18}{4}$

Add 2 on both sides we get;

$y-2+2=\frac{18}{4}+2$

Simplify:

 $y=\frac{26}{4} =6.5$

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.