Question

question
write the equation of the line in fully simplified slope - intercept form.
(here is a coordinate plane with a line plotted, the x - axis ranges from -12 to 12, and the y - axis ranges from -12 to 12)
answer attempt 2 out of 2

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, 10)\) (the y-intercept) and \((2, -4)\).

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

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, 10)\) and \((2, -4)\), we have \(x_1 = 0\), \(y_1 = 10\), \(x_2 = 2\), \(y_2 = -4\). So \(m = \frac{-4 - 10}{2 - 0} = \frac{-14}{2} = -7\).

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

The y-intercept is the value of \(y\) when \(x = 0\). From the point \((0, 10)\), we know that \(b = 10\).

Step4: Write the equation in slope - intercept form (\(y = mx + b\))

Substituting \(m = -7\) and \(b = 10\) into the slope - intercept form, we get \(y = -7x + 10\).

Answer:

\(y = -7x + 10\)