A line has a slope of 
4
7
 and passes through the point (
–
5,
–
3). Write its equation in slope-intercept form.

To write the equation of a line in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:

### Given:
- Slope \( m = \frac{4}{7} \)
- A point on the line: \( (-5, -3) \)

### Step 1: Use the point-slope form equation
The point-slope form of a line's equation is:

\[
y - y_1 = m(x - x_1)
\]

Where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. Substituting \( m = \frac{4}{7} \), \( x_1 = -5 \), and \( y_1 = -3 \):

\[
y - (-3) = \frac{4}{7}(x - (-5))
\]

This simplifies to:

\[
y + 3 = \frac{4}{7}(x + 5)
\]

### Step 2: Expand the equation
Distribute \( \frac{4}{7} \) on the right-hand side:

\[
y + 3 = \frac{4}{7}x + \frac{4}{7} \times 5
\]

\[
y + 3 = \frac{4}{7}x + \frac{20}{7}
\]

### Step 3: Solve for \( y \) to put it in

A line has a slope of 4/7 and passes through the point (-5, -3). Write its equation in slope-intercept form.

Learn how to write the equation of a line with a slope of 4/7 that passes through the point (-5, -3). This problem covers key algebraic concepts, including the slope-intercept form and point-slope form equations. Suitable for students in Grades 8-10.

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