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Vilka [71]
3 years ago
6

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

Mathematics
2 answers:
prohojiy [21]3 years ago
8 0
The points are at (8,0) and (0,6)
Novay_Z [31]3 years ago
8 0

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.


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