Question

Graph a line with a slope of -\dfrac34−

Answer 1

Given:

It is given that the slope $m=-\frac{3}{4}$ and contains the point (2,3)

We need to determine the graph of the line.

Equation of the line:

The equation of the line can be determined using the formula,

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

Substituting the point (2,3) and the slope $m=-\frac{3}{4}$ in the above formula, we get;

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

$y-3=-\frac{3}{4}x+\frac{3}{2}$

     $y=-\frac{3}{4}x+\frac{9}{2}$

Thus, the equation of the line is $y=-\frac{3}{4}x+\frac{9}{2}$

Graphing the line:

The equation of the line can be graphed by plotting the x and y intercepts.

The x - intercept is the value of x when y = 0. Thus, we get;

  $0=-\frac{3}{4}x+\frac{9}{2}$

$-\frac{9}{2}=-\frac{3}{4}x$

  $6=x$

Thus, the x - intercept is (6,0)

The y - intercept is the value of y when x = 0. Thus, we get;

$y=-\frac{3}{4}(0)+\frac{9}{2}$

$y=\frac{9}{2}$

$y=4.5$

Thus, the y - intercept is (0,4.5)

Hence, plotting these points and joining the line, we get the graph of the line $y=-\frac{3}{4}x+\frac{9}{2}$