Discover the Algebraic Equation of a Line Parallel to y=-3/4x+2 Through (8,2)

Q: What's the difference between parallel and perpendicular lines?

Parallel lines have the same slope and never intersect. Perpendicular lines have slopes that are negative reciprocals and intersect at 90°.

Q: Why can't I just use the same equation as the given line?

The given line $ y = -\frac{3}{4}x + 2 $ doesn't pass through (8,2)! Parallel lines have the same slope but different y-intercepts unless they're the same line.

Q: How do I find the y-intercept after using point-slope form?

After substituting into $ y - y_1 = m(x - x_1) $, solve for y to get slope-intercept form. The constant term becomes your y-intercept!

Q: Can I check my answer without substituting the point?

Yes! Verify that your line has slope $ -\frac{3}{4} $ and a different y-intercept than the original line. But substituting the point is the most reliable check.

Q: What if I get confused with the arithmetic?

Take it step by step! First distribute: $ -\frac{3}{4} \times 8 = -6 $. Then add: $ y = -\frac{3}{4}x + 6 + 2 = -\frac{3}{4}x + 8 $.

Parallel Lines with Point-Slope Method

Given the line parallel to the line

$y=-\frac{3}{4}x+2$

and passes through the point $(8,2)$ .

Which of the algebraic representations is the corresponding one for the given line?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:13 Let's find the algebraic form of the function.

00:16 This value represents the slope of the line.

00:21 Remember, parallel lines share the same slope.

00:30 Let's use the line equation here.

00:38 Next, plug in the given point as per the data provided.

00:45 Now, substitute the given slope into the line equation.

00:54 Keep going, solve to find where the line hits the Y-axis.

01:01 This point is the Y-intercept of the line.

01:08 Now, place the Y-intercept and slope back into the equation.

01:18 And there you have it, that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the line parallel to the line

$y=-\frac{3}{4}x+2$

and passes through the point $(8,2)$ .

Which of the algebraic representations is the corresponding one for the given line?

Step-by-step solution

To solve this problem, we'll determine the equation of the line that is parallel to $y = -\frac{3}{4}x+2$ and passes through the point $(8,2)$ .

Step 1: Identify the slope of the given line.
The slope ( $m$ ) of the line $y = -\frac{3}{4}x + 2$ is $-\frac{3}{4}$ , as it's the coefficient of $x$ .

Step 2: Use the point-slope form, $y - y_1 = m(x - x_1)$ , where $m = -\frac{3}{4}$ and the point $(x_1, y_1) = (8, 2)$ .

Substitute into the point-slope form:
$y - 2 = -\frac{3}{4}(x - 8)$

Step 3: Simplify this equation to obtain the slope-intercept form:
$y - 2 = -\frac{3}{4}x + \frac{3}{4} \times 8$

Calculate the right side:
$y - 2 = -\frac{3}{4}x + 6$

Add 2 to both sides to isolate $y$ :
$y = -\frac{3}{4}x + 6 + 2$
$y = -\frac{3}{4}x + 8$

This equation, $y = -\frac{3}{4}x + 8$ , is in slope-intercept form and matches choice 4.

Thus, the equation of the line parallel to $y = -\frac{3}{4}x + 2$ and passing through $(8, 2)$ is $\boxed{y = -\frac{3}{4}x + 8}$ .

Final Answer

$y=-\frac{3}{4}x+8$

Key Points to Remember

Essential concepts to master this topic

Parallel Rule: Parallel lines have identical slopes, different y-intercepts
Point-Slope Technique: Use $y - 2 = -\frac{3}{4}(x - 8)$ then simplify
Verification: Check point (8,2): $2 = -\frac{3}{4}(8) + 8 = 2$ ✓

Common Mistakes

Avoid these frequent errors

Using perpendicular slope instead of parallel slope
Don't flip the fraction to get $\frac{4}{3}$ = perpendicular line, not parallel! This creates a line that intersects the original at 90°, not runs alongside it. Always use the exact same slope for parallel lines.

Practice Quiz

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Which statement best describes the graph below?

FAQ

Everything you need to know about this question

What's the difference between parallel and perpendicular lines?

Parallel lines have the same slope and never intersect. Perpendicular lines have slopes that are negative reciprocals and intersect at 90°.

Why can't I just use the same equation as the given line?

The given line $y = -\frac{3}{4}x + 2$ doesn't pass through (8,2)! Parallel lines have the same slope but different y-intercepts unless they're the same line.

How do I find the y-intercept after using point-slope form?

After substituting into $y - y_1 = m(x - x_1)$ , solve for y to get slope-intercept form. The constant term becomes your y-intercept!

Can I check my answer without substituting the point?

Yes! Verify that your line has slope $-\frac{3}{4}$ and a different y-intercept than the original line. But substituting the point is the most reliable check.

What if I get confused with the arithmetic?

Take it step by step! First distribute: $-\frac{3}{4} \times 8 = -6$ . Then add: $y = -\frac{3}{4}x + 6 + 2 = -\frac{3}{4}x + 8$ .

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