Find a linear equation whose graph is the straight line with the given properties.
through

1,
−7
8

with slope
1
8
y(x) =

To find the linear equation \( y(x) \) of a line, we use the slope-intercept form of the equation of a line, which is:

\[
y = mx + b
\]

where:
- \( m \) is the slope
- \( b \) is the y-intercept.

Given:
- The slope \( m = \frac{1}{8} \)
- A point on the line \( (x_1, y_1) = (1, -7/8) \)

We can substitute these values into the equation and solve for \( b \).

### Step 1: Use the point-slope form:
We know the formula for point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Substitute \( m = \frac{1}{8} \), \( x_1 = 1 \), and \( y_1 = -\frac{7}{8} \):

\[
y - \left(-\frac{7}{8}\right) = \frac{1}{8}(x - 1)
\]

\[
y + \frac{7}{8} = \frac{1}{8}(x - 1)
\]

### Step 2: Simplify the equation:
Multiply out the right side:

\[
y + \frac{7}{8} = \frac{1}{8}x - \frac{1}{8}
\]

Now, subtract \( \frac{7}{8} \) from both sides:

\[
y = \frac{1}{8}x - \frac{1}{8} - \frac{7}{8}
\]

\[
y = \frac{1}{8}x - 1
\]

### Final equation:
The linear equation is:

\[
y(x) = \frac{1}{8}x - 1
\]

Would you like more details or have any further questions?

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Here are 5 related questions for further exploration:
1. How can we find the equation of a line given two points?
2. What is the significance of the slope in a linear equation?
3. How do you calculate the slope between two points?
4. How do parallel and perpendicular lines differ in terms of their slopes?
5. What is the point-slope form of a line, and when is it used?

**Tip:** Remember that the slope \( m \) describes how steep a line is and determines how the \( y \)-value changes as \( x \) increases.

Find a linear equation whose graph is the straight line with the given properties: through (1, −7/8) with slope 1/8

Learn how to find the equation of a line passing through the point (1, -7/8) with a slope of 1/8. This detailed step-by-step solution covers important concepts such as the slope-intercept form and point-slope form, suitable for students in Grades 8-10.

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