To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).

Step 1: Calculate the slope

The formula for the slope is:

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

Here, the points are (-2, 5) and (3, 10):

• $x_1 = -2, y_1 = 5$
• $x_2 = 3, y_2 = 10$

Substitute into the slope formula: $m = \frac{10 - 5}{3 - (-2)} = \frac{5}{5} = 1$

The slope $m = 1$.

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Step 2: Use the slope and a point to find the y-intercept

Using the slope-intercept form, $y = mx + b$, we substitute $m = 1$ and one of the points (e.g., $(-2, 5)$) into the equation to solve for $b$.

$y = mx + b$

Substitute $x = -2, y = 5, m = 1$: $5 = 1(-2) + b$

Simplify: $5 = -2 + b$

Add 2 to both sides: $b = 7$

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Step 3: Write the equation of the line

The equation is: $y = x + 7$

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Final Answer:

The equation of the line in slope-intercept form is: $\boxed{y = x + 7}$

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Would you like me to verify or expand on this?

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Here are 5 related questions:

1. How would you find the equation of a line parallel to $y = x + 7$ passing through a given point?
2. What is the equation of a line perpendicular to $y = x + 7$ that passes through the origin?
3. How do you convert this equation to standard form ($Ax + By = C$)?
4. What is the distance between the two points $(-2, 5)$ and $(3, 10)$?
5. How can you determine if a third point lies on the line $y = x + 7$?

Tip: To quickly verify your line equation, substitute both given points into $y = mx + b$ to confirm they satisfy the equation!