Question

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

Answer 1

Answer:

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 $\frac{1}{2}$ is,

$y-3=\frac{1}{2}(x-4)$

$2y - 6 = x - 4$

$x-2y = -6 + 4$

$x-2y = -2$

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.

Step-by-step 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":

$3=\frac{1}{2}(4)+b\\\\3-2=b\\\\b=1$

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:

$0=\frac{1}{2}x+1\\\\-1(2)=x\\\\x=-2$

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