The given equation is:

$y = 7x + 2$

This is already in slope-intercept form, which is written as:

$y = mx + b$

where:

• $m$ is the slope of the line.
• $b$ is the y-intercept, which is the value of $y$ when $x = 0$.

Step 1: Identify the slope

From the equation $y = 7x + 2$, the slope $m$ is 7.

Step 2: Identify the y-intercept

From the equation $y = 7x + 2$, the y-intercept $b$ is 2.

Final Answer:

• Slope: $7$
• Y-intercept: $2$

Graphing the Equation

1. Start by plotting the y-intercept (0, 2) on the graph.
2. Use the slope $7$, which means "rise over run" ($\frac{7}{1}$), to plot another point. From $(0, 2)$, move up 7 units and right 1 unit to find another point, $(1, 9)$.
3. Draw a straight line through these points to complete the graph.

Would you like me to create a visual graph for you or explain further?

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Additional Questions for Practice:

1. What happens to the slope if the equation changes to $y = -7x + 2$?
2. How do you find the x-intercept of the equation $y = 7x + 2$?
3. What is the equation of a line parallel to $y = 7x + 2$?
4. How does the graph change if the y-intercept is increased to $4$?
5. Can you rewrite this equation in standard form, $Ax + By = C$?

Tip:

When identifying the slope from $y = mx + b$, remember that the coefficient of $x$ ($m$) always indicates the steepness and direction of the line.