Write an equation of each line described below. Write the lines in slope-intercept form,
y
=
m
x
+
b
. Use integers and fractions in your answer, not decimals.

A) The line that passes through the point
P
(
0
,
−
5
)
and has a slope of
1
10
.

B) The line that passes through the point
P
(
2
,
1
)
and has a slope of
7
.

To write the equation of a line in slope-intercept form \( y = mx + b \), we need the slope \( m \) and the y-intercept \( b \). If we are given a point \( P(x_1, y_1) \) that lies on the line and the slope \( m \), we can use the point-slope form of the equation and then convert it to slope-intercept form.

### A) The line that passes through the point \( P(0, -5) \) and has a slope of \( \frac{1}{10} \).

Since the line passes through \( (0, -5) \), this point is the y-intercept. Therefore, \( b = -5 \). The slope is given as \( m = \frac{1}{10} \).

So, the equation is:
\[
y = \frac{1}{10}x - 5
\]

### B) The line that passes through the point \( P(2, 1) \) and has a slope of \( 7 \).

We use the point-slope form of the line equation:
\[
y - y_1 = m(x - x_1)
\]
Substituting \( (x_1, y_1) = (2, 1) \) and \( m = 7 \):
\[
y - 1 = 7(x - 2)
\]

Distribute and simplify to get the slope-intercept form:
\[
y - 1 = 7x - 14
\]
\[
y = 7x - 13
\]

### Final Answers:
A) \( y = \frac{1}{10}x - 5 \)

B) \( y = 7x - 13 \)

Would you like any details or further clarification on these solutions?

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Here are some related questions you might find interesting:
1. What is the slope-intercept form for a horizontal line passing through a given point?
2. How do you find the equation of a line if you are given two points?
3. What is the significance of the y-intercept in a linear equation?
4. How do you convert from slope-intercept form to standard form?
5. How do you determine if two lines are parallel based on their equations?

**Tip:** Always double-check that the y-intercept corresponds to the point where the line crosses the y-axis when writing equations in slope-intercept form.

Learn how to write equations of lines in slope-intercept form using specific examples. This page covers finding equations given points and slopes, including examples with integer and fractional coefficients. Suitable for Grades 7-9.

Math Problem Statement

Write an equation of each line described below. Write the lines in slope-intercept form, y

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