Write an equation of the line passing through the given point and satisfying the given condition. Give the equation​ (a) in​ slope-intercept form and​ (b) in standard form. ​(8​, 5​); parallel to 9xminusyequals8

We are given the point \((8, 5)\) and a condition that the line must be parallel to the line described by the equation \(9x - y = 8\).

### Step 1: Identify the slope of the given line
We need to find the slope of the line \(9x - y = 8\). First, rewrite the equation in slope-intercept form (\(y = mx + b\)), where \(m\) is the slope:

\[
9x - y = 8 \quad \text{(Original equation)}
\]

Solve for \(y\):

\[
y = 9x - 8
\]

From this, we can see that the slope of the given line is \(m = 9\).

### Step 2: Use the slope-point form to find the equation of the new line
Since the new line is parallel to the given line, it will have the same slope, \(m = 9\). The line also passes through the point \((8, 5)\). 

We can use the point-slope form of a line equation:

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

Substitute \(m = 9\), \(x_1 = 8\), and \(y_1 = 5\):

\[
y - 5 = 9(x - 8)
\]

### Step 3: Simplify to slope-intercept form
Expand and simplify the equation:

\[
y - 5 = 9x - 72
\]
\[
y = 9x - 72 + 5
\]
\[
y = 9x - 67
\]

Thus, the equation of the line in slope-intercept form is:

\[
\boxed{y = 9x - 67}
\]

### Step 4: Convert to standard form
The standard form of a line is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) is positive.

Starting with \(y = 9x - 67\), rearrange the terms to get:

\[
9x - y = 67
\]

Thus, the equation of the line in standard form is:

\[
\boxed{9x - y = 67}
\]

### Final Answers:
- (a) Slope-intercept form: \(y = 9x - 67\)
- (b) Standard form: \(9x - y = 67\)

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. Write the equation of a line passing through the point \((2, -3)\) and parallel to the line \(4x - y = 7\).
2. Find the equation of a line passing through \((1, 2)\) and perpendicular to the line \(y = -3x + 4\).
3. Determine the slope of the line parallel to \(5x + 2y = 10\).
4. Find the equation of a line passing through \((4, 1)\) and with a slope of \(-2\).
5. Convert the equation \(7x + 3y = 9\) into slope-intercept form.

**Tip:** A line parallel to another has the same slope, while a line perpendicular to it has the negative reciprocal of its slope.

Write an equation of the line passing through the given point and satisfying the given condition. Give the equation​ (a) in​ slope-intercept form and​ (b) in standard form. ​(8​, 5​); parallel to 9x - y = 8.

Learn how to find the equation of a line passing through the point (8, 5) that is parallel to 9x - y = 8. This solution explains how to determine the slope, apply the point-slope form, and convert to both slope-intercept and standard form. Suitable for students in Grades 8-10.

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