Question12. $5 x-2 y=-10$

Studdy Solution

STEP 1

What is this asking? We're going to graph the line represented by the equation $5x - 2y = -10$ . Watch out! Don't forget to solve for $y$ to make graphing easier!

STEP 2

1. Solve for $y$
2. Find the intercepts
3. Plot the intercepts
4. Draw the line

STEP 3

First, let's rearrange the equation to solve for $y$ .
We start with:
$5x - 2y = -10$

STEP 4

To isolate $y$ , we need to move $5x$ to the other side.
Subtract $5x$ from both sides:
$-2y = -5x - 10$

STEP 5

Now, divide everything by $-2$ to solve for $y$ :
$y = \frac{5}{2}x + 5$ This equation is now in the slope-intercept form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 6

Find the y-intercept by setting $x = 0$ in the equation $y = \frac{5}{2}x + 5$ :
$y = \frac{5}{2}(0) + 5 = 5$ So, the y-intercept is $(0, 5)$ .

STEP 7

Find the x-intercept by setting $y = 0$ in the original equation $5x - 2y = -10$ :
$5x - 2(0) = -10$ $5x = -10$ $x = -2$ So, the x-intercept is $(-2, 0)$ .

STEP 8

On your graph, plot the y-intercept at $(0, 5)$ .

STEP 9

Next, plot the x-intercept at $(-2, 0)$ .

STEP 10

Now, draw a straight line through the points $(0, 5)$ and $(-2, 0)$ .
This line represents the equation $5x - 2y = -10$ .

STEP 11

The graph of the equation $5x - 2y = -10$ is a straight line passing through the points $(0, 5)$ and $(-2, 0)$ .

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