Respuesta :

luisejr77

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

We can find "b" substituting the slope and coordinates of the (4,3) into thte equation  [tex]y=mx+b[/tex], and then solving for "b":

[tex]3=\frac{1}{2}(4)+b\\\\3-2=b\\\\b=1[/tex]

By definition, the line intersects the x-axis when "y" is zero.

Then, we need to substitute the y-intercept and [tex]y=0[/tex] into  [tex]y=mx+b[/tex] and then solve for "x" in order to find the x-intercept:

[tex]0=\frac{1}{2}x+1\\\\-1(2)=x\\\\x=-2[/tex]

Knowing the x-intercept and the y-intercept, we can graph the line (The graph is attached)

Ver imagen luisejr77

Answer:

Since, the equation of a line passes through [tex](x_1, y_1)[/tex] with slope m is,

[tex]y-y_1=m(x-x_1)[/tex]

Thus, the equation of line passes through (4, 3) with slope [tex]\frac{1}{2}[/tex] is,

[tex]y-3=\frac{1}{2}(x-4)[/tex]

[tex]2y - 6 = x - 4[/tex]

[tex]x-2y = -6 + 4[/tex]

[tex]x-2y = -2[/tex]

If x = 0,

[tex]-2y=-2\implies y =1[/tex]

Thus, the line intersects y-axis at (0, 1),

If y = 0,

[tex]x-2(0) = -2\implies x = - 2[/tex]

Thus, the line intersects x-axis at (-2, 0),

By joining the points (0, 1) and (-2, 0) we get the graph of the given line ( shown below )

Ver imagen slicergiza