Answer:
Point-slope form: An equation of a straight line in the form [tex]y -y_1 = m(x -x_1)[/tex];
where
m is the slope of the line and [tex](x_1, y_1)[/tex] are the coordinates of a given point on the line.
Given the equation: [tex]y-2=-\frac{3}{4}(x-6)[/tex] ......[1]
On comparing with Point slope form equation we have;
m = [tex]-\frac{3}{4}[/tex] 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;
[tex]0-2=-\frac{3}{4}(x-6)[/tex]
[tex]-2=-\frac{3}{4}(x-6)[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b +a\cdot c[/tex]
[tex]-2 = -\frac{3}{4}x + \frac{18}{4}[/tex]
Subtract [tex]\frac{18}{4}[/tex] on both sides we get;
[tex]-2-\frac{18}{4}= -\frac{3}{4}x + \frac{18}{4} -\frac{18}{4} [/tex]
Simplify:
[tex]-\frac{26}{4} = -\frac{3}{4}x[/tex]
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;
[tex]y-2=-\frac{3}{4}(0-6)[/tex]
[tex]y-2=\frac{18}{4}[/tex]
Add 2 on both sides we get;
[tex]y-2+2=\frac{18}{4}+2[/tex]
Simplify:
[tex]y=\frac{26}{4} =6.5[/tex]
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.
