Let's break down the problem step by step:

a) Find the x-intercept

The x-intercept occurs where the line crosses the x-axis. At this point, $y = 0$. So, let's substitute $y = 0$ into the equation:

$x - 7(0) = 14 \implies x = 14$

x-intercept: (14, 0)

b) Find the y-intercept

The y-intercept occurs where the line crosses the y-axis. At this point, $x = 0$. So, substitute $x = 0$ into the equation:

$0 - 7y = 14 \implies -7y = 14 \implies y = -2$

y-intercept: (0, -2)

c) Find the gradient (slope) of the line

The general form of the equation of a line is $Ax + By = C$, where the slope $m$ is given by:

$m = -\frac{A}{B}$

For the equation $x - 7y = 14$, $A = 1$ and $B = -7$. Therefore, the slope is:

$m = -\frac{1}{-7} = \frac{1}{7}$

Slope (gradient): $\frac{1}{7}$

d) Rewrite the given equation into slope-intercept form

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Let's solve the given equation for $y$:

Starting with $x - 7y = 14$:

$-7y = -x + 14$

$y = \frac{1}{7}x - 2$

Slope-intercept form: $y = \frac{1}{7}x - 2$

e) Indicate whether the line rises, falls, is horizontal, or is vertical

Since the slope of the line is positive ($\frac{1}{7}$), the line rises as it moves from left to right.

f) Sketch the line

We have the following points and information:

• x-intercept: (14, 0)
• y-intercept: (0, -2)
• Slope: $\frac{1}{7}$ (meaning the line rises slowly)

The line passes through the points (0, -2) and (14, 0), and it rises slowly as it moves from left to right.

Let me know if you'd like a visual sketch or more information about any of these steps.

Related questions:

1. How do you find the slope of a line from a set of two points?
2. What is the difference between the general form and slope-intercept form of a line?
3. How can you identify the slope of a line from its graph?
4. What does a negative slope represent in terms of the line's direction?
5. How do you find the equation of a line if you are given the slope and one point?

Tip:

When finding the intercepts, always set the opposite variable (x for the y-intercept, and y for the x-intercept) equal to zero to simplify calculations.