Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -7)\) (the y - intercept) and \((4, 0)\). We can also use other points like \((6, 3)\) or \((9, 8)\) to calculate the slope. Let's use \((0, -7)\) and \((4, 0)\).

Step2: Calculate the slope (\(m\))

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1=-7,x_2 = 4,y_2 = 0\) into the formula:
\(m=\frac{0-(-7)}{4 - 0}=\frac{7}{4}\)

Step3: Determine the y - intercept (\(b\))

The slope - intercept form of a line is \(y=mx + b\), where \(b\) is the y - intercept. From the point \((0, -7)\), when \(x = 0\), \(y=-7\). So \(b=-7\).

Step4: Write the equation in slope - intercept form

Substitute \(m=\frac{7}{4}\) and \(b = - 7\) into \(y=mx + b\).
We get \(y=\frac{7}{4}x-7\)

Answer:

\(y=\frac{7}{4}x - 7\)