Question 4:
A straight line that passes through and . The equation of the line is

Question

Question 4: A straight line that passes through $$ (0,5) $$ and $$ (4,17) $$. The equation of the line is

UpStudy AI · Accepted Answer

To find the equation of the straight line passing through the points $$(0, 5)$$ and $$(4, 17)$$, follow these steps:

### Step 1: Find the Slope ($$m$$)

The slope of a line passing through two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Substitute the given points into the formula:

$$
m = \frac{17 - 5}{4 - 0} = \frac{12}{4} = 3
$$

### Step 2: Use the Slope-Intercept Form

The slope-intercept form of a line is:

$$
y = mx + b
$$

We already have the slope ($$m = 3$$). To find $$b$$, the y-intercept, use one of the given points. Using $$(0, 5)$$:

$$
5 = 3(0) + b \
5 = b
$$

### Step 3: Write the Equation

Substitute $$m = 3$$ and $$b = 5$$ into the slope-intercept form:

$$
y = 3x + 5
$$

### **Final Answer**

$$
\boxed{y = 3x + 5}
$$
The equation of the line is $$ y = 3x + 5 $$.

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