Question Find the $$ x $$-intercept of the following line. $$ y=\frac{8}{7} x+4 $$

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UpStudy AI · Accepted Answer

To find the $$ x $$-intercept of the line given by the equation:

$$
y = \frac{8}{7}x + 4
$$

**Step 1: Understand the $$ x $$-Intercept**

The $$ x $$-intercept is the point where the line crosses the $$ x $$-axis. At this point, the value of $$ y $$ is **0**.

**Step 2: Set $$ y = 0 $$ and Solve for $$ x $$**

$$
0 = \frac{8}{7}x + 4
$$

Subtract 4 from both sides:

$$
-\frac{8}{7}x = 4
$$

**Step 3: Isolate $$ x $$**

Multiply both sides by $$ \frac{7}{8} $$ to solve for $$ x $$:

$$
x = 4 \times \left( -\frac{7}{8} \right)
$$

$$
x = -\frac{28}{8}
$$

Simplify the fraction:

$$
x = -\frac{7}{2} \quad \text{or} \quad -3.5
$$

**Step 4: Write the $$ x $$-Intercept as a Point**

The $$ x $$-intercept is the point where $$ y = 0 $$, so:

$$
\left( -\frac{7}{2},\ 0 \right) \quad \text{or} \quad (-3.5,\ 0)
$$

**Final Answer:**

The $$ x $$-intercept of the line $$ y = \frac{8}{7}x + 4 $$ is $$ \boxed{\left( -\frac{7}{2},\ 0 \right)} $$.
The $$ x $$-intercept is $$ \left( -\frac{7}{2},\ 0 \right) $$ or $$ (-3.5,\ 0) $$.

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Find the -intercept of the following line.

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Question Find the -intercept of the following line.