Question

find the slope, y-intercept, and equation for the following
1.
slope:______
y-intercept: ______
equation:______________
2
slope ______
y-intercept: ______
equation ______________
graph the following linear equations
slope - intercept form: $y = mx + b$
3 $y = 4x - 2$
$m = $____ $b = $____

1. $y = \frac{-2}{5}x + 3$

$m = $____ $b = $____

Explanation:

Problem 1 (First Graph)

Step1: Identify two points

From the graph, we can see the line passes through \((0, -7)\) (y-intercept) and \((3, -1)\) (we can also use other points, but these are clear). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, -7)\) and \((x_2,y_2)=(3, -1)\).
\(m=\frac{-1 - (-7)}{3 - 0}=\frac{6}{3}=2\)

Step2: Find y-intercept

The y-intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, -7)\), \(b=-7\).

Step3: Write the equation

Using slope - intercept form \(y=mx + b\), substitute \(m = 2\) and \(b=-7\). So the equation is \(y = 2x-7\).

Step1: Identify two points

The line passes through \((0, 6)\) (y - intercept) and \((10, 0)\) (x - intercept). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), let \((x_1,y_1)=(0, 6)\) and \((x_2,y_2)=(10, 0)\).
\(m=\frac{0 - 6}{10 - 0}=\frac{-6}{10}=-\frac{3}{5}\)

Step2: Find y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, 6)\), \(b = 6\).

Step3: Write the equation

Using slope - intercept form \(y=mx + b\), substitute \(m=-\frac{3}{5}\) and \(b = 6\). So the equation is \(y=-\frac{3}{5}x + 6\).

Step1: Identify \(m\) and \(b\) from slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y = 4x-2\), by comparing with \(y=mx + b\), we can see that \(m = 4\) and \(b=-2\).

Answer:

Slope: \(2\)
Y - intercept: \(-7\)
Equation: \(y = 2x-7\)

Problem 2 (Second Graph)