A line passes through the point

4, 2

and has a slope of

5/4

.

Write an equation in slope-intercept form for this line.

To write the equation of a line in slope-intercept form, we use the formula:

\[
y = mx + b
\]

Where:
- \( m \) is the slope.
- \( b \) is the y-intercept (the value of \( y \) when \( x = 0 \)).

We are given:
- The slope \( m = \frac{5}{4} \).
- A point on the line: \( (4, 2) \), which means when \( x = 4 \), \( y = 2 \).

To find the y-intercept \( b \), we substitute \( x = 4 \), \( y = 2 \), and \( m = \frac{5}{4} \) into the equation and solve for \( b \):

\[
2 = \frac{5}{4}(4) + b
\]

Simplify:

\[
2 = 5 + b
\]

Solve for \( b \):

\[
b = 2 - 5 = -3
\]

Now, substitute the slope \( m = \frac{5}{4} \) and the y-intercept \( b = -3 \) back into the slope-intercept form:

\[
y = \frac{5}{4}x - 3
\]

Thus, the equation of the line is:

\[
y = \frac{5}{4}x - 3
\]

Would you like more details or further clarification?

Here are some related questions:
1. How do you convert the equation to standard form?
2. How would the equation change if the slope was negative?
3. What is the significance of the slope in real-world problems?
4. How can you find the equation of a line parallel to this one?
5. How can you graph this equation starting from the slope and y-intercept?

**Tip:** When finding the equation of a line, always double-check by substituting the given point back into the final equation.

A line passes through the point (4, 2) and has a slope of 5/4. Write an equation in slope-intercept form for this line.

Learn how to write the equation of a line in slope-intercept form that passes through the point (4, 2) with a slope of 5/4. This problem demonstrates key algebraic concepts and how to find the y-intercept using the slope formula. Suitable for students in Grades 8-10.

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