Write an equation in point-slope form and slope-intercept form for: 1. passing through $$ (1,9) $$, slope $$ =2 $$ 3. passing through $$ (-4,-5) $$, slope $$ =\frac{3}{4} $$

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Certainly! Let's find the equations for both scenarios in **point-slope form** and **slope-intercept form**.

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### 1. Line Passing Through $$ (1, 9) $$ with Slope $$ m = 2 $$

**Point-Slope Form:**
The point-slope form of a line is given by:
$$ y - y_1 = m(x - x_1) $$
Plugging in the given point $$(1, 9)$$ and slope $$ m = 2 $$:
$$ y - 9 = 2(x - 1) $$

**Slope-Intercept Form:**
To convert to slope-intercept form $$ y = mx + b $$:
$$
\begin{align*}
y - 9 &= 2(x - 1) \
y - 9 &= 2x - 2 \
y &= 2x - 2 + 9 \
y &= 2x + 7
\end{align*}
$$

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### 2. Line Passing Through $$ (-4, -5) $$ with Slope $$ m = \frac{3}{4} $$

**Point-Slope Form:**
Using the point $$(-4, -5)$$ and slope $$ m = \frac{3}{4} $$:
$$ y - (-5) = \frac{3}{4}(x - (-4)) $$
$$ y + 5 = \frac{3}{4}(x + 4) $$

**Slope-Intercept Form:**
Converting to slope-intercept form:
$$
\begin{align*}
y + 5 &= \frac{3}{4}(x + 4) \
y + 5 &= \frac{3}{4}x + 3 \
y &= \frac{3}{4}x + 3 - 5 \
y &= \frac{3}{4}x - 2
\end{align*}
$$

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### **Summary**

1. **Passing through $$ (1, 9) $$, slope $$ = 2 $$:**
   - **Point-Slope Form:** $$ y - 9 = 2(x - 1) $$
   - **Slope-Intercept Form:** $$ y = 2x + 7 $$

2. **Passing through $$ (-4, -5) $$, slope $$ = \frac{3}{4} $$:**
   - **Point-Slope Form:** $$ y + 5 = \frac{3}{4}(x + 4) $$
   - **Slope-Intercept Form:** $$ y = \frac{3}{4}x - 2 $$
1. **Passing through $$ (1, 9) $$, slope $$ = 2 $$:** - **Point-Slope Form:** $$ y - 9 = 2(x - 1) $$ - **Slope-Intercept Form:** $$ y = 2x + 7 $$ 2. **Passing through $$ (-4, -5) $$, slope $$ = \frac{3}{4} $$:** - **Point-Slope Form:** $$ y + 5 = \frac{3}{4}(x + 4) $$ - **Slope-Intercept Form:** $$ y = \frac{3}{4}x - 2 $$

Write an equation in point-slope form and slope-intercept form for: 1. passing through \( (1,9) \), slope \( =2 \) 3. passing through \( (-4,-5) \), slope \( =\frac{3}{4} \)

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