Equation:
−
9
x
−
10
y
=
−
3

A) Write the equation in the form:
y
=
m
x
+
b

y
=

x
+

Enter the values of m and b in the appropriate boxes as integers or reduced fractions.

B) Use your equation from part A to find the ordered pair that lies on the line when
x
=
−
10
.

(
−
10
,
)
Enter your answer as an integer or a reduced fraction.

Let's first solve part A by rewriting the equation \( -9x - 10y = -3 \) in the slope-intercept form \( y = mx + b \).

### Part A:
Starting with the given equation:
\[
-9x - 10y = -3
\]

1. Isolate \( y \) on one side:
\[
-10y = 9x - 3
\]

2. Divide both sides by \( -10 \) to solve for \( y \):
\[
y = \frac{9x - 3}{-10}
\]

3. Simplify the equation:
\[
y = -\frac{9}{10}x + \frac{3}{10}
\]

Thus, the equation in slope-intercept form is:
\[
y = -\frac{9}{10}x + \frac{3}{10}
\]

In this form, \( m = -\frac{9}{10} \) (the slope) and \( b = \frac{3}{10} \) (the y-intercept).

### Part B:
Now, use the equation from part A to find the \( y \)-coordinate when \( x = -10 \).

Substitute \( x = -10 \) into the equation:
\[
y = -\frac{9}{10}(-10) + \frac{3}{10}
\]

Simplify:
\[
y = \frac{90}{10} + \frac{3}{10} = 9 + \frac{3}{10} = 9 + 0.3 = 9.3
\]

So, the ordered pair is:
\[
(-10, 9.3)
\]

If you prefer the fraction form, \( 9.3 = \frac{93}{10} \), so the ordered pair is \( (-10, \frac{93}{10}) \).

### Summary:
A) The equation is:
\[
y = -\frac{9}{10}x + \frac{3}{10}
\]
with \( m = -\frac{9}{10} \) and \( b = \frac{3}{10} \).

B) The ordered pair when \( x = -10 \) is:
\[
(-10, 9.3) \text{ or } (-10, \frac{93}{10})
\]

---

Do you have any questions or would you like further details?

Here are 5 related questions to expand on this concept:
1. How do you find the slope of a line given two points?
2. What does the slope represent in a real-world context?
3. How do you graph a line using the slope and y-intercept?
4. How can you rewrite an equation in standard form given the slope-intercept form?
5. What are the conditions for two lines to be parallel or perpendicular?

**Tip:** When converting an equation to slope-intercept form, focus on isolating \( y \) on one side.

Equation: -9x - 10y = -3. A) Write the equation in the form y = mx + b. Enter the values of m and b in the appropriate boxes as integers or reduced fractions. B) Use your equation from part A to find the ordered pair that lies on the line when x = -10.

Learn how to rewrite the equation -9x - 10y = -3 in slope-intercept form (y = mx + b) and find the ordered pair on the line when x = -10. This problem covers key algebraic concepts like slope and y-intercept, suitable for Grades 7-10 students.

Math Problem Statement

Equation: − 9 x − 10 y

A) Write the equation in the form: y

y

B) Use your equation from part A to find the ordered pair that lies on the line when x

Solution

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