Question

find an equation y = mx + b for the line whose graph is sketched ( click on the graph. the number m equals. the number b equals.

Explanation:

Step1: Find two points on the line

Let's assume two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line. From the graph, we can take \((0, - 5)\) and \((1,0)\) (by observing the intersection with axes).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \((x_1,y_1)=(0,-5)\) and \((x_2,y_2)=(1,0)\) into the formula, we get \(m=\frac{0 - (-5)}{1-0}=\frac{5}{1}=5\).

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

The equation of a line is \(y = mx + b\). The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,-5)\), when \(x = 0\), \(y=-5\), so \(b=-5\).

Answer:

The number \(m\) equals \(5\); The number \(b\) equals \(-5\)