Question

Graph a line that contains the point (4,3) and has a slope 1/2

Answer 1

Since, the equation of a line passes through
`(x_1, y_1)` with slope m is,

`y-y_1=m(x-x_1)`

Thus, the equation of line passes through (4, 3) with slope
`(1)/(2)` is,

`y-3=(1)/(2)(x-4)`

`2y - 6 = x - 4`

`x-2y = -6 + 4`

`x-2y = -2`

If x = 0,

`-2y=-2\implies y =1`

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

If y = 0,

`x-2(0) = -2\implies x = - 2`

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 )

Answer 2

Answer: The graph is attached.

Explanation:

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

`y=mx+b`

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
`y=mx+b`, and then solving for "b":

`3=(1)/(2)(4)+b\\\\3-2=b\\\\b=1`

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

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

`0=(1)/(2)x+1\\\\-1(2)=x\\\\x=-2`

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