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3241004551 [841]
3 years ago
9

Graph a line with a slope of -\dfrac34−

Mathematics
1 answer:
Leona [35]3 years ago
4 0

<u>Given</u><u>:</u>

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.

<u>Equation of the line:</u>

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}

<u>Graphing the line:</u>

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}

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