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The slope-intercept form is a way of writing the equation of a straight line. It is given by the formula: \[ y = mx + b \] Here:

• m is the slope of the line, which tells us how steep the line is. A positive slope means the line goes upward, while a negative slope means it goes downward.
• b is the y-intercept, which is the point where the line crosses the y-axis. This is the value of y when x is zero.
• y and x are the coordinates of any point on the line.

Using this form makes it easy to quickly identify both the slope and the y-intercept of a line.

To find the y-intercept of a line when the slope and a point on the line are given, you can follow these steps:1. **Substitute the given slope and coordinates into the slope-intercept equation:**

If you know the slope m and a point (x, y), you can plug these values into the slope-intercept form: \[ y = mx + b \].

2. **Solve for b:**

After substituting the values, you'll get an equation with b as the only unknown. Solve this equation to find the y-intercept. For example, given a slope m = -\frac{7}{4} and a point (4, 7), substitute these into the slope-intercept form:

\[ 7 = -\frac{7}{4} \times 4 + b \]

You then solve for b step-by-step:

• First compute: \[ -\frac{7}{4} \times 4 = -7 \]
• Substitute back:

\[ 7 = -7 + b \]

• Add 7 to both sides to isolate b:

\[ 7 + 7 = b \]

\[ b = 14 \]

Solving linear equations involves finding the unknown variables that make the equation true. Here are the steps used in solving the problem:

• **Identify the known values:** Find the slope and use the coordinates of the given point.
• **Substitute into the equation:** Use the known values to replace m, x, and y in the slope-intercept form.
• **Isolate the unknown:** Simplify the equation to find the unknown variable, in this case, the y-intercept b.

Learn the standard form of a linear equation and practice substituting and solving to build confidence.