Question

d graph the line $2x + 5y = -10$, following the

Explanation:

To graph the line \(2x + 5y=- 10\), we can find the \(x -\)intercept and \(y -\)intercept.

Step 1: Find the \(y -\)intercept

The \(y -\)intercept is the point where \(x = 0\). Substitute \(x=0\) into the equation \(2x + 5y=-10\)

\[

$$\begin{align*} 2(0)+5y&=- 10\\ 5y&=-10\\ y&=\frac{- 10}{5}\\ y&=-2 \end{align*}$$

\]

So the \(y -\)intercept is \((0,-2)\)

Step 2: Find the \(x -\)intercept

The \(x -\)intercept is the point where \(y = 0\). Substitute \(y = 0\) into the equation \(2x+5y=-10\)

\[

$$\begin{align*} 2x + 5(0)&=-10\\ 2x&=-10\\ x&=\frac{-10}{2}\\ x&=- 5 \end{align*}$$

\]

So the \(x -\)intercept is \((-5,0)\)

Step 3: Graph the line

Plot the points \((0,-2)\) (the \(y -\)intercept) and \((-5,0)\) (the \(x -\)intercept) on the coordinate plane. Then draw a straight line passing through these two points.

If we want to write the equation in slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the \(y -\)intercept):

Starting from \(2x+5y=-10\)

\[

$$\begin{align*} 5y&=-2x - 10\\ y&=-\frac{2}{5}x-2 \end{align*}$$

\]

The slope \(m =-\frac{2}{5}\) and the \(y -\)intercept \(b=-2\)

To graph using slope - intercept form, we start at the \(y -\)intercept \((0,-2)\). The slope \(m =-\frac{2}{5}\) means we move down 2 units (because the numerator is \(- 2\)) and then move 5 units to the right (because the denominator is \(5\)) to get another point \((5,-4)\) (or we can move up 2 units and 5 units to the left to get \((-5,0)\)) and then draw the line through these points.

Answer:

To graph the line \(2x + 5y=- 10\), we can find the \(x -\)intercept and \(y -\)intercept.

Step 1: Find the \(y -\)intercept

The \(y -\)intercept is the point where \(x = 0\). Substitute \(x=0\) into the equation \(2x + 5y=-10\)

\[

$$\begin{align*} 2(0)+5y&=- 10\\ 5y&=-10\\ y&=\frac{- 10}{5}\\ y&=-2 \end{align*}$$

\]

So the \(y -\)intercept is \((0,-2)\)

Step 2: Find the \(x -\)intercept

The \(x -\)intercept is the point where \(y = 0\). Substitute \(y = 0\) into the equation \(2x+5y=-10\)

\[

$$\begin{align*} 2x + 5(0)&=-10\\ 2x&=-10\\ x&=\frac{-10}{2}\\ x&=- 5 \end{align*}$$

\]

So the \(x -\)intercept is \((-5,0)\)

Step 3: Graph the line

Plot the points \((0,-2)\) (the \(y -\)intercept) and \((-5,0)\) (the \(x -\)intercept) on the coordinate plane. Then draw a straight line passing through these two points.

If we want to write the equation in slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the \(y -\)intercept):

Starting from \(2x+5y=-10\)

\[

$$\begin{align*} 5y&=-2x - 10\\ y&=-\frac{2}{5}x-2 \end{align*}$$

\]

The slope \(m =-\frac{2}{5}\) and the \(y -\)intercept \(b=-2\)

To graph using slope - intercept form, we start at the \(y -\)intercept \((0,-2)\). The slope \(m =-\frac{2}{5}\) means we move down 2 units (because the numerator is \(- 2\)) and then move 5 units to the right (because the denominator is \(5\)) to get another point \((5,-4)\) (or we can move up 2 units and 5 units to the left to get \((-5,0)\)) and then draw the line through these points.