Question

how to graph the inequality 5x-7y<-35

Answer 1

To graph the inequality \( 5x - 7y < -35 \), you can follow these steps:

### Step 1: Convert the inequality to an equation
First, convert the inequality to an equation by replacing the inequality sign with an equal sign:
\[ 5x - 7y = -35 \]

### Step 2: Find the intercepts
To graph the equation, you can find the x-intercept and y-intercept.

**For the x-intercept** (where \( y = 0 \)):
\[
5x - 7(0) = -35 \\
5x = -35 \\
x = -7
\]
So, the x-intercept is at the point \( (-7, 0) \).

**For the y-intercept** (where \( x = 0 \)):
\[
5(0) - 7y = -35 \\
-7y = -35 \\
y = 5
\]
So, the y-intercept is at the point \( (0, 5) \).

### Step 3: Plot the line
Draw a dashed line through the points \( (-7, 0) \) and \( (0, 5) \). The dashed line indicates that the points on the line are not included in the solution set (since the original inequality is \( < \)).

### Step 4: Determine which side of the line to shade
To find out which side of the line to shade, pick a test point not on the line. A common choice is the origin \( (0, 0) \).

Substituting \( (0, 0) \) into the original inequality:
\[
5(0) - 7(0) < -35 \\
0 < -35 \quad (\text{This is false})
\]
Since the test point \( (0, 0) \) does not satisfy the inequality, shade the opposite side of the line.

### Step 5: Final graph
You should have a dashed line representing \( 5x - 7y = -35 \) and shading in the region that does **not** include the origin. This shaded area represents all the solutions to the inequality \( 5x - 7y < -35 \).

And that's how you graph the inequality!