Question

2-33 On graph paper, graph a line with y-intercept (0,-4) and x-intercept (3,0). Find the Help equation of the line.

Answer 1

$y\text{ = }\frac{4}{3}x\text{ -4}$

Explanation:

Given points:

(0, -4) and (3, 0)

Plotting the points:

To find the equation of the line, we will use the formula:

y = mx + b

where m = slope

b = y-intercept

Using the slope formula:

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$$\begin{gathered} x_1=0,y_1=-4,x_2=3,y_2\text{ = 0} \\ m\text{ = }\frac{0-(-4)}{3\text{ - 0}} \\ m\text{ = }\frac{0+4}{3} \\ m\text{ = 4/3} \end{gathered}$

y-intercept is the value of y when x = 0

From the points, given, when x = 0, y = -4

Hence, y-intercept = y = -4

The equation becomes:

$\begin{gathered} y\text{ = }\frac{4}{3}x\text{ + (-4)} \\ y\text{ = }\frac{4}{3}x\text{ -4} \end{gathered}$