To analyze the equation $y = 1 + 7x$, we can identify its slope, y-intercept, and x-intercept.

1. Slope

The equation $y = 1 + 7x$ is in slope-intercept form $y = mx + b$, where:

• $m$ is the slope.
• $b$ is the y-intercept.

In this case, $m = 7$, so the slope is $7$.

2. Y-intercept

The y-intercept is the point where the graph crosses the y-axis, which occurs when $x = 0$.

Substitute $x = 0$ into the equation: $y = 1 + 7(0) = 1$ Thus, the y-intercept is $(0, 1)$.

3. X-intercept

The x-intercept is the point where the graph crosses the x-axis, which occurs when $y = 0$.

Set $y = 0$ and solve for $x$: $0 = 1 + 7x$ $7x = -1$ $x = -\frac{1}{7}$ Thus, the x-intercept is $\left( -\frac{1}{7}, 0 \right)$.

Summary:

• Slope: 7
• Y-intercept: $(0, 1)$
• X-intercept: $\left( -\frac{1}{7}, 0 \right)$

Would you like more details or further clarification?

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Here are 5 related questions to expand on this topic:

1. How does the slope of a line affect its steepness?
2. What happens if the slope is negative?
3. Can you find the intercepts for $y = 2 - 3x$?
4. How would you graph the equation $y = 1 + 7x$?
5. How can you rewrite the equation $y = 1 + 7x$ in standard form?

Tip: When finding intercepts, remember that the x-intercept occurs when $y = 0$, and the y-intercept occurs when $x = 0$.