$y+6=\frac{3}{4}(x+4)$

Question

06-11-2026
Mathematics

Answered

$y+6=\frac{3}{4}(x+4)$

Verified Answer :

Related Questions

Im doing homewrok so I need help Ok so I need to find all the metaphors in a piece of text So would A giant of a man be one Because I am so confused p

Toby sells paintings for 20 Mark sells his paintings for 14 each and charges a fee of 18 for framing How much paintings have to be bought for Toby and Mark to h

Which sentence uses italics or quotation marks correctly A My sister loves Dream a Little Dream of Me by The Mamas and the Papas B Jake cant sit still when the

Which of the following produce intrinsic factor A parietal cells B zymogenic cells C mucous neck cells D enteroendocrine cells

what is the difference between a prime number and a complex number

2. For each of the following functions, find the domain and range, and sketch the graph of: A) $f(x) = x^{1/6}$ B) $h(x) = x^{1/7}$ 3. Find the absolute va

Which of the following is a step in the scientific method? A. Ask a question B. Conduct background research C. Construct a hypothesis D. Perform an experi

Solve for $p$. $p + 4 = 60$ $p = \square$

what type of suffrage did women gain in New York in 1917

luke lives 04 kilometers from the skating rink mark lives 025 kilometers from the skating rink who lives closer to the rink

GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-06T08:27:02-05:00

Identify the slope $m = \frac{3}{4}$ and a point $(-4, -6)$ from the given point-slope form.
Distribute the slope and isolate $y$ to convert to slope-intercept form.
The resulting slope-intercept equation is $y = \frac{3}{4}x - 3$.
Final linear equation is $\boxed{y = \frac{3}{4}x - 3}$.

Explanation

Analyzing the Equation

The given equation is $y + 6 = \frac{3}{4}(x + 4)$. This is in the point-slope form $y - y_1 = m(x - x_1)$, which describes a straight line with slope $m$ passing through the point $(x_1, y_1)$. Comparing the given equation to this form, we can determine the key characteristics of the line.

Identifying Slope and Point

By comparing $y + 6 = \frac{3}{4}(x + 4)$ with $y - y_1 = m(x - x_1)$, we can identify the slope and a point on the line.

The slope $m$ is the coefficient $\frac{3}{4}$.
Rewriting the equation to match the form exactly, we have $y - (-6) = \frac{3}{4}(x - (-4))$.
Thus, the point $(x_1, y_1)$ on the line is $(-4, -6)$.

Converting to Slope-Intercept Form

To express the equation in slope-intercept form $y = mx + b$, we isolate $y$:

Distribute the $\frac{3}{4}$ into the parentheses:

$y + 6 = \frac{3}{4}x + \frac{3}{4} \times 4$
$y + 6 = \frac{3}{4}x + 3$

Subtract 6 from both sides to solve for $y$:

$y = \frac{3}{4}x + 3 - 6$
$y = \frac{3}{4}x - 3$
The equation is now in the form $y = \frac{3}{4}x - 3$.

Conclusion and Final Answer

From the slope-intercept form $y = \frac{3}{4}x - 3$, we can clearly identify:

The slope is $m = \frac{3}{4}$.
The y-intercept is $-3$, which corresponds to the point $(0, -3)$.

The final line equation is $\boxed{y = \frac{3}{4}x - 3}$.

Examples

This concept is crucial for understanding linear relationships in real-world scenarios. For example, if a taxi charges a base fee and a per-mile rate, you can model the total cost using a linear equation. If the taxi charges a base fee of $\$3$ (the y-intercept) and $\$0.75$ per mile (the slope), the total cost $y$ for a distance $x$ is $y = 0.75x + 3$. By mastering slope-intercept form, you can quickly analyze these types of costs and make informed decisions about your travel expenses.