Question

for the above graph,
a) find the slope (m). \\( m = \\)
b) find the y-intercept (b). \\( b = \\)
c) write the equation of the line in slope-intercept form (i.e., \\( y = mx + b \\)).
\\( y = \\)

Explanation:

Step1: Find two points on the line

From the graph, we can identify two points: \((0, -5)\) (the y - intercept) and \((5, 0)\).

Step2: Calculate the slope \(m\)

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 5)\) and \((x_2,y_2)=(5,0)\). Then \(m=\frac{0-(-5)}{5 - 0}=\frac{5}{5}=1\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-5)\), we can see that \(b=-5\).

Step4: Write the equation in slope - intercept form

The slope - intercept form is \(y=mx + b\). We know that \(m = 1\) and \(b=-5\), so the equation is \(y=1x-5\) or \(y=x - 5\).

Answer:

s:
a) \(m=\boxed{1}\)
b) \(b=\boxed{-5}\)
c) \(y=\boxed{x - 5}\)