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The slope-intercept form is a special way of writing equations of straight lines. It is called so because it clearly shows both the slope of the line and where the line crosses the y-axis. The standard form of this equation is given by: \( y = mx + b \). Here, the variable \( m \) represents the slope of the line, which indicates how steep the line is. The variable \( b \) is the y-intercept, which is the point where the line crosses the y-axis. Converting an equation into slope-intercept form often requires isolating the \( y \)-variable.
In our example, the original equation is \( 2x - 5y = -10 \). To put it in slope-intercept form, we need to solve for \( y \):

• Subtract \( 2x \) from both sides to get \( -5y = -2x - 10 \).
• Divide every term by \( -5 \) to isolate \( y \). This results in the equation \( y = \frac{2}{5}x + 2 \).

Now the equation is in slope-intercept form \( y = mx + b \).

The y-intercept is the point where a line crosses the y-axis. This point is crucial for graphing because it gives a definite starting point on the coordinate plane. In the equation \( y = \frac{2}{5}x + 2 \), the y-intercept \( b \) is 2.
To plot the y-intercept:

• Locate the y-axis on your graph.
• Find the point where \( y = 2 \). This is the point \( (0, 2) \).
• Place a dot at this point.

This point means when \( x = 0 \), the value of \( y \) is 2. It is the starting point for graphing the line.

The slope of a line is a measure of its steepness. It tells you how much \( y \) changes for a change in \( x \). Mathematically, it is the ratio of the rise (change in y) to the run (change in x). In our slope-intercept form equation \( y = \frac{2}{5}x + 2 \), the slope \( m \) is \( \frac{2}{5} \).
To interpret the slope \( \frac{2}{5} \):

• For every 5 units you move to the right (positive direction along the \( x \)-axis), you move 2 units up (positive direction along the \( y \)-axis).
• This rise over run, \( \frac{2}{5} \), tells you the line goes up 2 units for every 5 units it goes to the right.

To use the slope to plot another point:

• Start from the y-intercept \( (0, 2) \).
• Move up by 2 units and then 5 units to the right.
• Plot this new point.

Connect the points with a straight line to complete the graph.